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This commit is contained in:
arielherself 2025-01-07 16:45:32 +08:00
parent e87bc2b483
commit 116635e918
Signed by: arielherself
SSH Key Fingerprint: SHA256:AK3cyo9tFsp7Mox7K0sYphleC8hReXhnRKxwuDT5LBc
15 changed files with 4265 additions and 349 deletions

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@ -540,29 +540,24 @@ void prep() {
// __attribute__((target("popcnt")))
void solve() {
int n;
unordered_set<string> oc;
while (1) {
read(int, n);
unordered_map<string, int> mp;
for (int i = 0; i < n; ++i) {
read(int, m);
while (m--) {
read(string, s);
if (s[0] >= '0' and s[0] <= '9') {
n = stoi(s);
break;
}
string nw;
for (auto&& c : s) {
if (c >= 'A' and c <= 'Z') {
nw += c - 'A' + 'a';
} else if (c >= 'a' and c <= 'z') {
nw += c;
mp[s] += 1;
}
}
oc.emplace(nw);
vector<string> res;
for (auto&& [x, c] : mp) {
if (c == n) {
res.emplace_back(x);
}
while (n--) {
read(string, s);
oc.erase(s);
}
cout << oc.size() << '\n';
sort(res.begin(), res.end());
cout << res.size() << '\n';
putvec_eol(res);
}
int main() {

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@ -535,14 +535,29 @@ void dump() {}
void dump_ignore() {}
void prep() {
}
constexpr int N = 5e5 + 10;
ll fact[N], factrev[N + 1], s[N + 1];
void prep() {}
// __attribute__((target("popcnt")))
void solve() {
read(string, s);
string s1(s.rbegin(), s.rend());
cout << s1 << '\n';
read(int, n, k);
auto work = [&n] (int k) -> ll {
vector<ll> dp(n + 1);
dp[0] = 1;
for (int i = 1; i <= n; ++i) {
dp[i] = dp[i - 3];
if (i - k - 1 >= 0) {
dp[i] -= dp[i - k - 1];
}
dp[i] = mod(dp[i], PRIME);
dp[i] = (dp[i] + dp[i - 1]) % PRIME;
}
return mod(dp[n] - dp[n - 1], PRIME);
};
ll cnt = mod(work(k) - work(k - 1), PRIME);
}
int main() {

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@ -538,50 +538,186 @@ void dump_ignore() {}
void prep() {
}
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
vector<int> a(n + 1);
a[0] = 2200;
adj(ch, n);
for (int i = 1; i <= n; ++i) {
read(int, f, x);
edge(ch, i, f);
a[i] = x;
struct SA {
int n;
std::vector<int> sa, rk, lc;
vector<vector<int>> st;
SA(std::string s) {
n = s.size();
sa.resize(n);
lc.resize(n - 1);
rk.resize(n);
std::iota(sa.begin(), sa.end(), 0);
sort_by_key(sa.begin(), sa.end(), expr(s[i], int i));
rk[sa[0]] = 0;
for (int i = 1; i < n; i++) {
rk[sa[i]] = rk[sa[i - 1]] + (s[sa[i]] != s[sa[i - 1]]);
}
vector<ll> ps(n + 1);
vector<bool> valid(n + 1);
{
auto dfs = [&] (auto dfs, int v, int pa) -> void {
int son = 0;
for (auto&& u : ch[v]) {
if (u == pa) continue;
son += 1;
dfs(dfs, u, v);
ps[v] += ps[u];
int k = 1;
std::vector<int> tmp, cnt(n);
tmp.reserve(n);
while (rk[sa[n - 1]] < n - 1) {
tmp.clear();
for (int i = 0; i < k; i++) {
tmp.push_back(n - k + i);
}
if (not son) {
ps[v] = a[v];
for (auto i : sa) {
if (i >= k) {
tmp.push_back(i - k);
}
}
std::fill(cnt.begin(), cnt.end(), 0);
for (int i = 0; i < n; i++) {
cnt[rk[i]]++;
}
for (int i = 1; i < n; i++) {
cnt[i] += cnt[i - 1];
}
for (int i = n - 1; i >= 0; i--) {
sa[--cnt[rk[tmp[i]]]] = tmp[i];
}
std::swap(rk, tmp);
rk[sa[0]] = 0;
for (int i = 1; i < n; i++) {
rk[sa[i]] = rk[sa[i - 1]] + (tmp[sa[i - 1]] < tmp[sa[i]] || sa[i - 1] + k == n || tmp[sa[i - 1] + k] < tmp[sa[i] + k]);
}
k *= 2;
}
for (int i = 0, j = 0; i < n; i++) {
if (rk[i] == 0) {
j = 0;
} else {
valid[v] = 1;
for (j -= j > 0; i + j < n && sa[rk[i] - 1] + j < n && s[i + j] == s[sa[rk[i] - 1] + j]; ) {
j++;
}
lc[rk[i] - 1] = j;
}
}
int m = lc.size();
int lgm = lg2(m);
st = vector(lgm + 1, vector<int>(m));
st[0] = lc;
for (int j = 0; j < lgm; j++) {
for (int i = 0; i + (2 << j) <= m; i++) {
st[j + 1][i] = std::min(st[j][i], st[j][i + (1 << j)]);
}
};
dfs(dfs, 0, 0);
}
if (ps[0] > a[0]) {
cout << "NO\n";
return;
}
sort(a.begin() + 1, a.end());
sort(ps.begin() + 1, ps.end());
for (int i = 1; i <= n; ++i) {
if (ps[i] > a[i]) {
cout << "NO\n";
return;
int rmq(int l, int r) {
int k = lg2(r - l);
return std::min(st[k][l], st[k][r - (1 << k)]);
}
__attribute__((target("lzcnt")))
int lcp(int i, int j) {
if (i == j || i == n || j == n) {
return std::min(n - i, n - j);
}
int a = rk[i];
int b = rk[j];
if (a > b) {
std::swap(a, b);
}
return std::min({n - i, n - j, rmq(a, b)});
}
int lcs(int i, int j) {
if (i == j || i == 0 || j == 0) {
return std::min(i, j);
}
int a = rk[n + n - i];
int b = rk[n + n - j];
if (a > b) {
std::swap(a, b);
}
return std::min({i, j, rmq(a, b)});
}
};
// __attribute__((target("popcnt")))
void solve() {
read(int, m);
read(string, s, t);
string p = s + '#' + t;
SA sa(p);
// vector<int> pp = calc_next(p);
vector<ll> pw(5 * m + 1);
pw[0] = 1;
for (int i = 1; i <= 5 * m; ++i) {
pw[i] = pw[i - 1] * 26 % PRIME;
}
vector<int> ps = calc_z(s);
// debug(ps);
vector<int> pt = calc_z(t);
int n1 = s.size(), n2 = t.size();
for (int i = 1; i <= m; ++i) {
int tot = 2 * i + n1 + n2;
if (tot % 2) {
cout << "0 ";
continue;
}
int half = tot / 2;
int left = i;
int right = i + n1 - 1;
int l2 = i + n1 + i;
int f = 1;
if (n2 > half) {
if (pt[half] >= n2 - half) {
;;
} else {
f = 0;
}
}
cout << "YES\n";
// deb(n1, half, ps[half]);
if (n1 > half) {
if (ps[half] >= n1 - half) {
;;
} else {
f = 0;
}
}
int cs = max(l2 - half, left), ce = min(half - 1, right);
if (cs <= ce) {
int ds = cs + half - l2, de = ce + half - l2;
cs -= left, ce -= left;
if (sa.lcp(cs, n1 + 1 + ds) >= ce - cs + 1) {
;;
} else {
f = 0;
}
}
if (f == 0) {
cout << 0 << ' ';
continue;
}
vector<pii> segs;
segs.emplace_back(max(0, l2 - half), half - 1);
segs.emplace_back(left, min(half - 1, right));
if (right >= half) {
segs.emplace_back(0, right - half);
}
sort(segs.begin(), segs.end());
int rr = -1;
int rem = 0;
for (auto&& [l, r] : segs) {
if (l > rr) {
rem += l - rr - 1;
}
chmax(rr, r);
}
rem += half - 1 - rr;
// debug(rem);
cout << pw[rem] << ' ';
}
}
int main() {

612
src/bin/cf-771d.cc Normal file
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@ -0,0 +1,612 @@
// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
#pragma GCC optimize("Ofast,unroll-loops")
/************* This code requires C++17. ***************/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
template <typename T> struct argument_type;
template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = __float128; // up to 1e-9 precision in binary search
using pii = pair<int, int>; using pil = pair<int, ll>; using pid = pair<int, ld>;
using pli = pair<ll, int>; using pll = pair<ll, ll>; using pld = pair<ll, ld>;
using pdi = pair<ld, int>; using pdl = pair<ld, ll>; using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>; using tiil = tuple<int, int, ll>; using tiid = tuple<int, int, ld>;
using tili = tuple<int, ll, int>; using till = tuple<int, ll, ll>; using tild = tuple<int, ll, ld>;
using tidi = tuple<int, ld, int>; using tidl = tuple<int, ld, ll>; using tidd = tuple<int, ld, ld>;
using tlii = tuple<ll, int, int>; using tlil = tuple<ll, int, ll>; using tlid = tuple<ll, int, ld>;
using tlli = tuple<ll, ll, int>; using tlll = tuple<ll, ll, ll>; using tlld = tuple<ll, ll, ld>;
using tldi = tuple<ll, ld, int>; using tldl = tuple<ll, ld, ll>; using tldd = tuple<ll, ld, ld>;
using tdii = tuple<ld, int, int>; using tdil = tuple<ld, int, ll>; using tdid = tuple<ld, int, ld>;
using tdli = tuple<ld, ll, int>; using tdll = tuple<ld, ll, ll>; using tdld = tuple<ld, ll, ld>;
using tddi = tuple<ld, ld, int>; using tddl = tuple<ld, ld, ll>; using tddd = tuple<ld, ld, ld>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll PRIMELL = 901017227882342239LL;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937_64 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!((var) == (val))) (var) = (val); else
#define continue_or(var, val) __AS_PROCEDURE(if ((var) == (val)) continue; (var) = (val);)
#define break_or(var, val) __AS_PROCEDURE(if ((var) == (val)) break; (var) = (val);)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
safe_hash hasher;
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
auto h = hasher(x);
res1 = (res1 + h * pw1) % __array_hash_mdl1;
res2 = (res2 + h * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
// add declarations to avoid circular dependency
template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
template<typename T> ostream& operator<<(ostream&, const vector<T>&);
std::ostream& operator<<(std::ostream&, const int128&);
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
for (size_t i = 0; i < N; ++i) in >> a[i];
return in;
}
template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
for (auto&& i : a) out << i << ' ';
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::type>(cin), (n), (a).begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
#define deb(...) debug(make_tuple(__VA_ARGS__))
/* pops */
template <typename Container>
inline auto poptop(Container& q) {
auto ret = q.top();
q.pop();
return ret;
}
template <typename Container>
inline auto popback(Container& q) {
auto ret = q.back();
q.pop_back();
return ret;
}
template <typename Container>
inline auto popfront(Container& q) {
auto ret = q.front();
q.pop_front();
return ret;
}
/* math */
template <typename return_t>
return_t qpow(ll b, ll p) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
return_t half = qpow<return_t>(b, p / 2);
if (p % 2 == 1) return half * half * b;
else return half * half;
}
// dynamic modulus
ll qpow(ll b, ll p, ll mod) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
ll half = qpow(b, p / 2, mod);
if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
else return half * half % mod;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wparentheses"
// Accurately find `i` 'th root of `n` (taking the floor)
inline ll root(ll n, ll i) {
ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
while (l < r) {
ll mid = l + r + 1 >> 1;
if (qpow<int128>(mid, i) <= n) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
#pragma GCC diagnostic pop
#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
__attribute__((target("lzcnt")))
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
template <typename T>
T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(const string& s, const string& t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(const string& s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(int128(lhs.val) * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename T, typename U>
bool chmax(T& lhs, const U& rhs) {
bool ret = lhs < rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
template <typename T, typename U>
bool chmin(T& lhs, const U& rhs) {
bool ret = lhs > rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
#define functor(func) ([&](auto&&... val) \
noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
{return func(std::forward<decltype(val)>(val)...);})
#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
}
#define initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
namespace detail {
template <typename T, std::size_t...Is>
constexpr std::array<T, sizeof...(Is)>
make_array(const T& value, std::index_sequence<Is...>) {
return {{(static_cast<void>(Is), value)...}};
}
}
template <typename T, std::size_t N>
constexpr std::array<T, N> __initarray(const T& value) {
return detail::make_array(value, std::make_index_sequence<N>());
}
/*******************************************************/
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {
}
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
vector<int> a(n);
for (int i = 0; i < n; ++i) {
read(char, c);
if (c == 'V') {
a[i] = 0;
} else if (c == 'K') {
a[i] = 1;
} else {
a[i] = 2;
}
}
// vector dp(n, vector(n, vector(n + 1, vector<int>(n + 1, INF))));
vector<vector<vector<vector<vector<int>>>>> dp(n);
for (int i = 0; i < n; ++i) {
dp[i].resize(n - i);
for (int j = 0; j < n - i; ++j) {
dp[i][j].resize(j + 2);
for (int k = 0; k <= j + 1; ++k) {
dp[i][j][k].resize(j + 1 - k + 1);
for (int l = 0; l <= j + 1 - k; ++l) {
dp[i][j][k][l].resize((j + 1) / 2 + 1);
}
}
}
}
for (int i = n - 1; ~i; --i) {
for (int j = i; j < n; ++j) {
if (i == j) {
dp[i][0][a[i] == 0][a[i] == 1][0] = 0;
} else {
if (a[i] == 0) {
for (int k = 0; k <= j - i; ++k) {
for (int l = 0; l <= j - i - k; ++l) {
for (int m = 0; m <= (j - i) / 2; ++m) {
}
}
}
}
}
}
}
}
int main() {
#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
static_assert(false, "incompatible compiler variant detected.");
#endif
untie;
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t != (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
#pragma GCC optimize("Ofast,unroll-loops")
/************* This code requires C++17. ***************/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
template <typename T> struct argument_type;
template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = __float128; // up to 1e-9 precision in binary search
using pii = pair<int, int>; using pil = pair<int, ll>; using pid = pair<int, ld>;
using pli = pair<ll, int>; using pll = pair<ll, ll>; using pld = pair<ll, ld>;
using pdi = pair<ld, int>; using pdl = pair<ld, ll>; using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>; using tiil = tuple<int, int, ll>; using tiid = tuple<int, int, ld>;
using tili = tuple<int, ll, int>; using till = tuple<int, ll, ll>; using tild = tuple<int, ll, ld>;
using tidi = tuple<int, ld, int>; using tidl = tuple<int, ld, ll>; using tidd = tuple<int, ld, ld>;
using tlii = tuple<ll, int, int>; using tlil = tuple<ll, int, ll>; using tlid = tuple<ll, int, ld>;
using tlli = tuple<ll, ll, int>; using tlll = tuple<ll, ll, ll>; using tlld = tuple<ll, ll, ld>;
using tldi = tuple<ll, ld, int>; using tldl = tuple<ll, ld, ll>; using tldd = tuple<ll, ld, ld>;
using tdii = tuple<ld, int, int>; using tdil = tuple<ld, int, ll>; using tdid = tuple<ld, int, ld>;
using tdli = tuple<ld, ll, int>; using tdll = tuple<ld, ll, ll>; using tdld = tuple<ld, ll, ld>;
using tddi = tuple<ld, ld, int>; using tddl = tuple<ld, ld, ll>; using tddd = tuple<ld, ld, ld>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll PRIMELL = 901017227882342239LL;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937_64 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!((var) == (val))) (var) = (val); else
#define continue_or(var, val) __AS_PROCEDURE(if ((var) == (val)) continue; (var) = (val);)
#define break_or(var, val) __AS_PROCEDURE(if ((var) == (val)) break; (var) = (val);)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
safe_hash hasher;
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
auto h = hasher(x);
res1 = (res1 + h * pw1) % __array_hash_mdl1;
res2 = (res2 + h * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
// add declarations to avoid circular dependency
template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
template<typename T> ostream& operator<<(ostream&, const vector<T>&);
std::ostream& operator<<(std::ostream&, const int128&);
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
for (size_t i = 0; i < N; ++i) in >> a[i];
return in;
}
template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
for (auto&& i : a) out << i << ' ';
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::type>(cin), (n), (a).begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
#define deb(...) debug(make_tuple(__VA_ARGS__))
/* pops */
template <typename Container>
inline auto poptop(Container& q) {
auto ret = q.top();
q.pop();
return ret;
}
template <typename Container>
inline auto popback(Container& q) {
auto ret = q.back();
q.pop_back();
return ret;
}
template <typename Container>
inline auto popfront(Container& q) {
auto ret = q.front();
q.pop_front();
return ret;
}
/* math */
template <typename return_t>
return_t qpow(ll b, ll p) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
return_t half = qpow<return_t>(b, p / 2);
if (p % 2 == 1) return half * half * b;
else return half * half;
}
// dynamic modulus
ll qpow(ll b, ll p, ll mod) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
ll half = qpow(b, p / 2, mod);
if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
else return half * half % mod;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wparentheses"
// Accurately find `i` 'th root of `n` (taking the floor)
inline ll root(ll n, ll i) {
ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
while (l < r) {
ll mid = l + r + 1 >> 1;
if (qpow<int128>(mid, i) <= n) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
#pragma GCC diagnostic pop
#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
__attribute__((target("lzcnt")))
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
template <typename T>
T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(const string& s, const string& t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(const string& s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(int128(lhs.val) * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename T, typename U>
bool chmax(T& lhs, const U& rhs) {
bool ret = lhs < rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
template <typename T, typename U>
bool chmin(T& lhs, const U& rhs) {
bool ret = lhs > rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
#define functor(func) ([&](auto&&... val) \
noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
{return func(std::forward<decltype(val)>(val)...);})
#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
}
#define initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
namespace detail {
template <typename T, std::size_t...Is>
constexpr std::array<T, sizeof...(Is)>
make_array(const T& value, std::index_sequence<Is...>) {
return {{(static_cast<void>(Is), value)...}};
}
}
template <typename T, std::size_t N>
constexpr std::array<T, N> __initarray(const T& value) {
return detail::make_array(value, std::make_index_sequence<N>());
}
/*******************************************************/
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {
}
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
readvec(int, a, n);
readvec(int, b, n);
ll sa = accumulate(a.begin(), a.end(), ll(0));
ll sb = accumulate(b.begin(), b.end(), ll(0));
auto check = [&] (const vector<int>& idx) {
ll ca = 0, cb = 0;
for (auto&& i : idx) {
ca += a[i];
cb += b[i];
}
return 2 * ca > sa and 2 * cb > sb;
};
vector<int> perm(n);
iota(perm.begin(), perm.end(), 0);
while (1) {
shuffle(perm.begin(), perm.end(), rd);
vector<int> curr(perm.begin(), perm.begin() + n / 2 + 1);
if (check(curr)) {
cout << n / 2 + 1 << '\n';
transform(curr.begin(), curr.end(), curr.begin(), expr(x + 1, auto&& x));
putvec(curr);
break;
}
}
}
int main() {
#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
static_assert(false, "incompatible compiler variant detected.");
#endif
untie;
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t != (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

@ -1 +1 @@
Subproject commit b33b8ed3f4e64e62b354eb3acf0f92ec93a41f75
Subproject commit dfd419ac9502baf7d916ecbca18ae11521be72d9

View File

@ -538,40 +538,71 @@ void dump_ignore() {}
void prep() {
}
template <typename T> struct point {
T x, y;
point() : x(), y() {}
point(const pair<T, T>& a) : x(a.first), y(a.second) {}
point(const T& x, const T& y) : x(x), y(y) {}
inline T square() const { return x * x + y * y; }
inline long double norm() const { return sqrt((long double)(square())); }
inline point operator+(const point& rhs) const { return point(x + rhs.x, y + rhs.y); }
inline point operator-(const point& rhs) const { return point(x - rhs.x, y - rhs.y); }
inline point operator+() const { return *this; }
inline point operator-() const { return point(-x, -y); }
inline point operator*(const T& a) const { return point(x * a, y * a); }
inline T operator*(const point& rhs) const { return x * rhs.y - y * rhs.x; }
inline point operator/(const T& a) const { return point(x / a, y / a); }
inline point& operator+=(const point& rhs) { x += rhs.x, y += rhs.y; return *this; }
inline point& operator-=(const point& rhs) { x -= rhs.x, y -= rhs.y; return *this; }
inline point& operator*=(const T& a) { x *= a, y *= a; return *this; }
inline point& operator/=(const T& a) { x /= a, y /= a; return *this; }
inline bool operator==(const point& rhs) const { return x == rhs.x and y == rhs.y; }
inline bool operator!=(const point& rhs) const { return not (*this == rhs); }
inline bool operator<(const point& rhs) const { return pair(x, y) < pair(rhs.x, rhs.y); }
inline bool operator<=(const point& rhs) const { return *this < rhs or *this == rhs; }
inline bool operator>(const point& rhs) const { return not (*this <= rhs); }
inline bool operator>=(const point& rhs) const { return not (*this < rhs); }
static inline long double slope(const point& a, const point& b) {
if (a.x == b.x) return INFLL;
return (long double)(a.y - b.y) / (a.x - b.x);
}
// distance from point `a` to line `l--r`
static inline long double dist(const point& a, const point& l, const point& r) {
return area(a, l, r) * 2 / (l - r).norm();
}
static inline long double area(const point& a, const point& b, const point& c) {
return abs((b - a) * (c - a)) / ld(2);
}
friend inline istream& operator>>(istream& in, point& a) {
return in >> a.x >> a.y;
}
friend inline ostream& operator<<(ostream& out, const point& a) {
return out << a.x << ' ' << a.y;
}
};
// __attribute__((target("popcnt")))
void solve() {
read(int, n, q);
readvec(int, a, n);
read(int, _);
int prod = 1;
for (auto&& x : a) prod *= x;
if (prod == 0) {
cout << "Yes\n";
} else {
constexpr int D = 5;
vector dp(n, vector(2 * D + 1, vector<int>(2)));
dp[0][D + a[0]][a[0] == 1] = 1;
for (int i = 1; i < n; ++i) {
for (int j = -D; j <= D; ++j) {
for (int k = 0; k < 2; ++k) {
// continue
int nw = (k ? 1 : -1) * a[i];
if (j - (k ? 1 : -1) + nw >= -D and j - (k ? 1 : -1) + nw <= D) {
dp[i][j - (k ? 1 : -1) + nw + D][nw == 1] or_eq dp[i - 1][j + D][k];
}
// new segment
if (j + a[i] >= -D and j + a[i] <= D) {
dp[i][j + a[i] + D][a[i] == 1] or_eq dp[i - 1][j + D][k];
}
}
}
}
if (dp[n - 1][D][0] or dp[n - 1][D][1]) {
cout << "Yes\n";
} else {
cout << "No\n";
}
}
using point = point<long double>;
read(int, xa, ya);
deb(xa, ya);
point a(xa, ya);
read(point, b);
read(point, c, d);
point e((a.x + b.x) / ld(2), (a.y + b.y) / ld(2));
cout << fixed << setprecision(50);
debug(c - e);
debug(d - e);
debug((long double)point::area(e, c, d));
cout << (long double)point::dist(e, c, d) << '\n';
}
int main() {

View File

@ -538,238 +538,38 @@ void dump_ignore() {}
void prep() {
}
namespace tarjan {
struct mutex_cond {
int v1; bool cond1;
int v2; bool cond2;
mutex_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
};
struct inclusive_cond {
int v1; bool cond1;
int v2; bool cond2;
inclusive_cond(int v1, bool cond1, int v2, bool cond2) : v1(v1), cond1(cond1), v2(v2), cond2(cond2) {}
};
// Returns the mapping between vertices and their affiliated sccs.
vector<int> scc(const vector<vector<int>>& ch) {
int n = ch.size();
int cnt = 0, scn = 0;
vector<int> dfn(n), low(n), vis(n), st;
vector<int> br(n);
auto tarjan = [&] (auto tarjan, int v) -> void {
dfn[v]=low[v]=++cnt;
st.push_back(v);
vis[v]=1;
for(const auto&u:ch[v])
if(!dfn[u]) tarjan(tarjan, u),low[v]=min(low[v],low[u]);
else if(vis[u])low[v]=min(low[v],dfn[u]);
if(dfn[v]==low[v]){
++scn;
int u;
do u=st.back(), st.pop_back(),vis[u]=0,br[u]=scn; while(u!=v);
}
};
for (int i = 0; i < n; ++i) {
if (!dfn[i]) {
tarjan(tarjan, i);
}
}
return br;
}
// This method can eliminate redundant edges or self-loops
vector<vector<int>> build_scc(const vector<vector<int>>& ch) {
int n = ch.size();
auto br = scc(ch);
int cnt = *max_element(br.begin(), br.end());
vector<unordered_set<int, safe_hash>> rb(cnt + 1);
for (int i = 0; i < n; ++i) {
for (auto&& u : ch[i]) {
if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
}
}
vector<vector<int>> res(cnt + 1);
for (int i = 1; i <= cnt; ++i) {
res[i] = vector<int>(rb[i].begin(), rb[i].end());
}
return res;
}
// This method can eliminate redundant edges or self-loops
// return form: (scc size, children of scc)
vector<pair<size_t, vector<int>>> build_scc_with_size(const vector<vector<int>>& ch) {
int n = ch.size();
auto br = scc(ch);
int cnt = *max_element(br.begin(), br.end());
vector<unordered_set<int, safe_hash>> rb(cnt + 1);
for (int i = 0; i < n; ++i) {
for (auto&& u : ch[i]) {
if (br[i] != br[u]) rb[br[i]].emplace(br[u]);
}
}
vector<pair<size_t, vector<int>>> res(cnt + 1);
for (int i = 1; i <= cnt; ++i) {
res[i].second = vector<int>(rb[i].begin(), rb[i].end());
}
for (int i = 1; i <= n; ++i) {
res[br[i]].first += 1;
}
return res;
}
// indices start from 1, result has `n` items
optional<vector<bool>> solve_twosat(int n, const vector<mutex_cond>& conditions) {
vector<vector<int>> ch(2 * n + 1);
for (auto&& [v1, cond1, v2, cond2] : conditions) {
ch[(1 ^ cond1) * n + v1].emplace_back(cond2 * n + v2);
ch[(1 ^ cond2) * n + v2].emplace_back(cond1 * n + v1);
}
auto sccno = scc(ch);
for (int i = 1; i <= n; ++i) {
if (sccno[i] == sccno[i + n]) {
return nullopt;
}
}
vector<bool> res;
for (int i = 1; i <= n; ++i) {
if (sccno[i] < sccno[i + n]) {
res.emplace_back(false);
} else {
res.emplace_back(true);
}
}
return res;
};
// indices start from 1, result has `n` items
optional<vector<bool>> solve_twosat(int n, const vector<inclusive_cond>& conditions) {
vector<mutex_cond> trans_conds;
for (auto&& [v1, cond1, v2, cond2] : conditions) {
trans_conds.emplace_back(v1, cond1, v2, not cond2);
}
return solve_twosat(n, trans_conds);
}
// Returns if each vertex is a cut vertex
// All indices start from 1
vector<int> cut_v(const vector<vector<int>>& ch) {
int n = ch.size() - 1;
vector<bool> vis(n + 1);
vector<int> low(n + 1), dfn(n + 1), flag(n + 1);
int cnt = 0;
auto dfs = [&] (auto dfs, int v, int pa) -> void {
vis[v] = 1;
low[v] = dfn[v] = ++cnt;
int child = 0;
for (auto&& u : ch[v]) {
if (not vis[u]) {
++child;
dfs(dfs, u, v);
low[v] = min(low[v], low[u]);
if (pa != v and low[u] >= dfn[v] and not flag[v]) {
flag[v] = 1;
}
} else if (u != pa) {
low[v] = min(low[v], dfn[u]);
}
}
if (pa == v and child >= 2 and not flag[v]) {
flag[v] = 1;
}
};
for (int i = 1; i <= n; ++i) {
if (not dfn[i]) {
dfs(dfs, i, 0);
}
}
return flag;
}
}
class quick_union {
private:
vector<size_t> c, sz;
public:
quick_union(size_t n) : c(n), sz(n) {
iota(c.begin(), c.end(), 0);
sz.assign(n, 1);
}
size_t query(size_t i) {
if (c[i] != i) c[i] = query(c[i]);
return c[i];
}
void merge(size_t i, size_t j) {
if (connected(i, j)) return;
sz[query(j)] += sz[query(i)];
c[query(i)] = query(j);
}
bool connected(size_t i, size_t j) {
return query(i) == query(j);
}
size_t query_size(size_t i) {
return sz[query(i)];
}
};
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
adj(ch, n);
quick_union qu(n + 1);
vector<pii> raw;
for (int i = 1; i <= n; ++i) {
read(int, j);
Edge(ch, i, j);
raw.emplace_back(i, j);
qu.merge(i, j);
vector<int> res;
int start = 1;
if (n % 8 == 1) {
res.emplace_back(1);
start = 2;
} else if (n % 8 == 2) {
res = { 1, 2 };
start = 3;
} else if (n % 8 == 3) {
res = { 1, 2, 3 };
start = 4;
} else if (n % 8 == 4) {
res = { 1, 2, 3, 4 };
start = 5;
} else if (n % 8 == 5) {
res = { 5, 2, 1, 4, 3 };
start = 6;
} else if (n % 8 == 6) {
res = { 5, 2, 3, 6, 1, 4 };
start = 7;
} else if (n % 8 == 7) {
res = { 1, 4, 7, 2, 3, 6, 5 };
start = 8;
}
vector<vector<int>> cc(n + 1);;
for (int i = 1; i <= n; ++i) {
cc[qu.query(i)].emplace_back(i);
for (int i = start; i + 7 <= n; i += 8) {
vector<int> curr = { i + 2, i + 7, i + 4, i + 1, i + 6, i + 3, i, i + 5 };
res.insert(res.end(), curr.begin(), curr.end());
}
vector<vector<vector<int>>> nch(n + 1);
for (int i = 1; i <= n; ++i) {
nch[i].assign(cc[i].size() + 1, {});
}
int cnt = 0;
vector<int> mapped(n + 1);
for (auto&& ns : cc) {
if (ns.empty()) continue;
cnt += 1;
int m = ns.size();
for (int i = 0; i < m; ++i) {
mapped[ns[i]] = i + 1;
}
}
for (auto&& [u, v] : raw) {
Edge(nch[qu.query(u)], mapped[u], mapped[v]);
}
int res = cnt - 1;
for (int i = 1; i <= n; ++i) {
if (cc[i].empty()) continue;
auto scc = tarjan::scc(nch[i]);
int f = 1;
for (int j = 2; j <= cc[i].size(); ++j) {
if (scc[j] != scc[1]) {
f = 0;
break;
}
}
if (f == 0) {
res += 1;
}
}
cout << res << '\n';
putvec(res);
}
int main() {

View File

@ -527,7 +527,7 @@ constexpr std::array<T, N> __initarray(const T& value) {
}
/*******************************************************/
#define SINGLE_TEST_CASE
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
@ -538,18 +538,129 @@ void dump_ignore() {}
void prep() {
}
template<typename T>
struct BIT {
int n;
vector<T> c;
BIT(size_t n) : n(n), c(n + 1) {}
void add(size_t i, const T& k) {
while (i <= n) {
c[i] += k;
i += lowbit(i);
}
}
T getsum(size_t i) {
T res = {};
while (i) {
res += c[i];
i -= lowbit(i);
}
return res;
}
};
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
read(int, a, b, c);
int res = 0;
readvec(pii, s, n);
read(int, d);
for (auto&& [x, y] : s) {
if (x + y >= c) continue;
if (min(a, x + d) + y >= c) res += 1;
read(int, n, m);
vector a(n, vector<int>(m));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
cin >> a[i][j];
}
}
vector<pii> rows;
vector<vector<int>> cols;
bool row_sorted = 1, col_sorted = 1;
int prev_mx = -1;
for (int i = 0; i < n; ++i) {
int mn = INF, mx = -INF;
for (int j = 0; j < m; ++j) {
chmin(mn, a[i][j]);
chmax(mx, a[i][j]);
}
vector<int> idx(m);
iota(idx.begin(), idx.end(), 0);
sort_by_key(idx.begin(), idx.end(), expr(a[i][j], auto&& j));
cols.emplace_back(idx);
rows.emplace_back(mn, mx);
if (mn > prev_mx) {
;;
} else {
row_sorted = 0;
}
prev_mx = mx;
}
for (int i = 1; i < m; ++i) {
if (cols[0][i] > cols[0][i - 1]) {
;;
} else {
col_sorted = 0;
}
}
vector<int> rowidx(n), colidx(m);
iota(rowidx.begin(), rowidx.end(), 0);
iota(colidx.begin(), colidx.end(), 0);
sort_by_key(rowidx.begin(), rowidx.end(), expr(rows[i], auto i));
sort_by_key(colidx.begin(), colidx.end(), expr(a[0][i], auto i));
for (int i = 1; i < n; ++i) {
if (rows[rowidx[i]].first < rows[rowidx[i - 1]].second or cols[rowidx[i]] != cols[rowidx[i - 1]]) {
cout << "NSFW\n";
return;
}
}
int rowinv = 0, colinv = 0;
{
vector<bool> vis(n);
int cnt;
{
auto dfs = [&] (auto dfs, int v) -> void {
vis[v] = 1;
cnt += 1;
if (not vis[rowidx[v]]) dfs(dfs, rowidx[v]);
};
for (int i = 0; i < n; ++i) {
if (not vis[i]) {
cnt = 0;
dfs(dfs, i);
rowinv += cnt - 1;
}
}
}
}
{
vector<bool> vis(m);
int cnt;
{
auto dfs = [&] (auto dfs, int v) -> void {
vis[v] = 1;
cnt += 1;
if (not vis[colidx[v]]) dfs(dfs, colidx[v]);
};
for (int i = 0; i < m; ++i) {
if (not vis[i]) {
cnt = 0;
dfs(dfs, i);
colinv += cnt - 1;
}
}
}
}
if (rowinv % 2 == colinv % 2) {
// fox loses
if (n == 2) {
cout << "CAT\n";
} else {
cout << "NSFW\n";
}
} else {
// cat loses
if (m == 2 or rowinv == 1 and colinv == 0) {
cout << "FOX\n";
} else {
cout << "NSFW\n";
}
}
cout << res<< '\n';
}
int main() {

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// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
#pragma GCC optimize("Ofast,unroll-loops")
/************* This code requires C++17. ***************/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
template <typename T> struct argument_type;
template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = __float128; // up to 1e-9 precision in binary search
using pii = pair<int, int>; using pil = pair<int, ll>; using pid = pair<int, ld>;
using pli = pair<ll, int>; using pll = pair<ll, ll>; using pld = pair<ll, ld>;
using pdi = pair<ld, int>; using pdl = pair<ld, ll>; using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>; using tiil = tuple<int, int, ll>; using tiid = tuple<int, int, ld>;
using tili = tuple<int, ll, int>; using till = tuple<int, ll, ll>; using tild = tuple<int, ll, ld>;
using tidi = tuple<int, ld, int>; using tidl = tuple<int, ld, ll>; using tidd = tuple<int, ld, ld>;
using tlii = tuple<ll, int, int>; using tlil = tuple<ll, int, ll>; using tlid = tuple<ll, int, ld>;
using tlli = tuple<ll, ll, int>; using tlll = tuple<ll, ll, ll>; using tlld = tuple<ll, ll, ld>;
using tldi = tuple<ll, ld, int>; using tldl = tuple<ll, ld, ll>; using tldd = tuple<ll, ld, ld>;
using tdii = tuple<ld, int, int>; using tdil = tuple<ld, int, ll>; using tdid = tuple<ld, int, ld>;
using tdli = tuple<ld, ll, int>; using tdll = tuple<ld, ll, ll>; using tdld = tuple<ld, ll, ld>;
using tddi = tuple<ld, ld, int>; using tddl = tuple<ld, ld, ll>; using tddd = tuple<ld, ld, ld>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll PRIMELL = 901017227882342239LL;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937_64 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!((var) == (val))) (var) = (val); else
#define continue_or(var, val) __AS_PROCEDURE(if ((var) == (val)) continue; (var) = (val);)
#define break_or(var, val) __AS_PROCEDURE(if ((var) == (val)) break; (var) = (val);)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
safe_hash hasher;
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
auto h = hasher(x);
res1 = (res1 + h * pw1) % __array_hash_mdl1;
res2 = (res2 + h * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
// add declarations to avoid circular dependency
template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
template<typename T> ostream& operator<<(ostream&, const vector<T>&);
std::ostream& operator<<(std::ostream&, const int128&);
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
for (size_t i = 0; i < N; ++i) in >> a[i];
return in;
}
template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
for (auto&& i : a) out << i << ' ';
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::type>(cin), (n), (a).begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
#define deb(...) debug(make_tuple(__VA_ARGS__))
/* pops */
template <typename Container>
inline auto poptop(Container& q) {
auto ret = q.top();
q.pop();
return ret;
}
template <typename Container>
inline auto popback(Container& q) {
auto ret = q.back();
q.pop_back();
return ret;
}
template <typename Container>
inline auto popfront(Container& q) {
auto ret = q.front();
q.pop_front();
return ret;
}
/* math */
template <typename return_t>
return_t qpow(ll b, ll p) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
return_t half = qpow<return_t>(b, p / 2);
if (p % 2 == 1) return half * half * b;
else return half * half;
}
// dynamic modulus
ll qpow(ll b, ll p, ll mod) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
ll half = qpow(b, p / 2, mod);
if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
else return half * half % mod;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wparentheses"
// Accurately find `i` 'th root of `n` (taking the floor)
inline ll root(ll n, ll i) {
ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
while (l < r) {
ll mid = l + r + 1 >> 1;
if (qpow<int128>(mid, i) <= n) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
#pragma GCC diagnostic pop
#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
__attribute__((target("lzcnt")))
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
template <typename T>
T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(const string& s, const string& t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(const string& s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(int128(lhs.val) * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename T, typename U>
bool chmax(T& lhs, const U& rhs) {
bool ret = lhs < rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
template <typename T, typename U>
bool chmin(T& lhs, const U& rhs) {
bool ret = lhs > rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
#define functor(func) ([&](auto&&... val) \
noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
{return func(std::forward<decltype(val)>(val)...);})
#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
}
#define initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
namespace detail {
template <typename T, std::size_t...Is>
constexpr std::array<T, sizeof...(Is)>
make_array(const T& value, std::index_sequence<Is...>) {
return {{(static_cast<void>(Is), value)...}};
}
}
template <typename T, std::size_t N>
constexpr std::array<T, N> __initarray(const T& value) {
return detail::make_array(value, std::make_index_sequence<N>());
}
/*******************************************************/
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {
}
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
unordered_map<string, int> mp;
for (int i = 0; i < n; ++i) {
read(int, m);
while (m--) {
read(string, s);
mp[s] += 1;
}
}
vector<string> res;
for (auto&& [x, c] : mp) {
if (c == n) {
res.emplace_back(x);
}
}
sort(res.begin(), res.end());
cout << res.size() << '\n';
putvec_eol(res);
}
int main() {
#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
static_assert(false, "incompatible compiler variant detected.");
#endif
untie;
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t != (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
#pragma GCC optimize("Ofast,unroll-loops")
/************* This code requires C++17. ***************/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
template <typename T> struct argument_type;
template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = __float128; // up to 1e-9 precision in binary search
using pii = pair<int, int>; using pil = pair<int, ll>; using pid = pair<int, ld>;
using pli = pair<ll, int>; using pll = pair<ll, ll>; using pld = pair<ll, ld>;
using pdi = pair<ld, int>; using pdl = pair<ld, ll>; using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>; using tiil = tuple<int, int, ll>; using tiid = tuple<int, int, ld>;
using tili = tuple<int, ll, int>; using till = tuple<int, ll, ll>; using tild = tuple<int, ll, ld>;
using tidi = tuple<int, ld, int>; using tidl = tuple<int, ld, ll>; using tidd = tuple<int, ld, ld>;
using tlii = tuple<ll, int, int>; using tlil = tuple<ll, int, ll>; using tlid = tuple<ll, int, ld>;
using tlli = tuple<ll, ll, int>; using tlll = tuple<ll, ll, ll>; using tlld = tuple<ll, ll, ld>;
using tldi = tuple<ll, ld, int>; using tldl = tuple<ll, ld, ll>; using tldd = tuple<ll, ld, ld>;
using tdii = tuple<ld, int, int>; using tdil = tuple<ld, int, ll>; using tdid = tuple<ld, int, ld>;
using tdli = tuple<ld, ll, int>; using tdll = tuple<ld, ll, ll>; using tdld = tuple<ld, ll, ld>;
using tddi = tuple<ld, ld, int>; using tddl = tuple<ld, ld, ll>; using tddd = tuple<ld, ld, ld>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll PRIMELL = 901017227882342239LL;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937_64 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!((var) == (val))) (var) = (val); else
#define continue_or(var, val) __AS_PROCEDURE(if ((var) == (val)) continue; (var) = (val);)
#define break_or(var, val) __AS_PROCEDURE(if ((var) == (val)) break; (var) = (val);)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
safe_hash hasher;
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
auto h = hasher(x);
res1 = (res1 + h * pw1) % __array_hash_mdl1;
res2 = (res2 + h * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
// add declarations to avoid circular dependency
template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
template<typename T> ostream& operator<<(ostream&, const vector<T>&);
std::ostream& operator<<(std::ostream&, const int128&);
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
for (size_t i = 0; i < N; ++i) in >> a[i];
return in;
}
template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
for (auto&& i : a) out << i << ' ';
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::type>(cin), (n), (a).begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
#define deb(...) debug(make_tuple(__VA_ARGS__))
/* pops */
template <typename Container>
inline auto poptop(Container& q) {
auto ret = q.top();
q.pop();
return ret;
}
template <typename Container>
inline auto popback(Container& q) {
auto ret = q.back();
q.pop_back();
return ret;
}
template <typename Container>
inline auto popfront(Container& q) {
auto ret = q.front();
q.pop_front();
return ret;
}
/* math */
template <typename return_t>
return_t qpow(ll b, ll p) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
return_t half = qpow<return_t>(b, p / 2);
if (p % 2 == 1) return half * half * b;
else return half * half;
}
// dynamic modulus
ll qpow(ll b, ll p, ll mod) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
ll half = qpow(b, p / 2, mod);
if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
else return half * half % mod;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wparentheses"
// Accurately find `i` 'th root of `n` (taking the floor)
inline ll root(ll n, ll i) {
ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
while (l < r) {
ll mid = l + r + 1 >> 1;
if (qpow<int128>(mid, i) <= n) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
#pragma GCC diagnostic pop
#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
__attribute__((target("lzcnt")))
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
template <typename T>
T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(const string& s, const string& t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(const string& s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(int128(lhs.val) * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename T, typename U>
bool chmax(T& lhs, const U& rhs) {
bool ret = lhs < rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
template <typename T, typename U>
bool chmin(T& lhs, const U& rhs) {
bool ret = lhs > rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
#define functor(func) ([&](auto&&... val) \
noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
{return func(std::forward<decltype(val)>(val)...);})
#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
}
#define initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
namespace detail {
template <typename T, std::size_t...Is>
constexpr std::array<T, sizeof...(Is)>
make_array(const T& value, std::index_sequence<Is...>) {
return {{(static_cast<void>(Is), value)...}};
}
}
template <typename T, std::size_t N>
constexpr std::array<T, N> __initarray(const T& value) {
return detail::make_array(value, std::make_index_sequence<N>());
}
/*******************************************************/
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {
}
struct SA {
int n;
std::vector<int> sa, rk, lc;
vector<vector<int>> st;
SA(std::string s) {
n = s.size();
sa.resize(n);
lc.resize(n - 1);
rk.resize(n);
std::iota(sa.begin(), sa.end(), 0);
sort_by_key(sa.begin(), sa.end(), expr(s[i], int i));
rk[sa[0]] = 0;
for (int i = 1; i < n; i++) {
rk[sa[i]] = rk[sa[i - 1]] + (s[sa[i]] != s[sa[i - 1]]);
}
int k = 1;
std::vector<int> tmp, cnt(n);
tmp.reserve(n);
while (rk[sa[n - 1]] < n - 1) {
tmp.clear();
for (int i = 0; i < k; i++) {
tmp.push_back(n - k + i);
}
for (auto i : sa) {
if (i >= k) {
tmp.push_back(i - k);
}
}
std::fill(cnt.begin(), cnt.end(), 0);
for (int i = 0; i < n; i++) {
cnt[rk[i]]++;
}
for (int i = 1; i < n; i++) {
cnt[i] += cnt[i - 1];
}
for (int i = n - 1; i >= 0; i--) {
sa[--cnt[rk[tmp[i]]]] = tmp[i];
}
std::swap(rk, tmp);
rk[sa[0]] = 0;
for (int i = 1; i < n; i++) {
rk[sa[i]] = rk[sa[i - 1]] + (tmp[sa[i - 1]] < tmp[sa[i]] || sa[i - 1] + k == n || tmp[sa[i - 1] + k] < tmp[sa[i] + k]);
}
k *= 2;
}
for (int i = 0, j = 0; i < n; i++) {
if (rk[i] == 0) {
j = 0;
} else {
for (j -= j > 0; i + j < n && sa[rk[i] - 1] + j < n && s[i + j] == s[sa[rk[i] - 1] + j]; ) {
j++;
}
lc[rk[i] - 1] = j;
}
}
int m = lc.size();
int lgm = lg2(m);
st = vector(lgm + 1, vector<int>(m));
st[0] = lc;
for (int j = 0; j < lgm; j++) {
for (int i = 0; i + (2 << j) <= m; i++) {
st[j + 1][i] = std::min(st[j][i], st[j][i + (1 << j)]);
}
}
}
int rmq(int l, int r) {
int k = lg2(r - l);
return std::min(st[k][l], st[k][r - (1 << k)]);
}
__attribute__((target("lzcnt")))
int lcp(int i, int j) {
if (i == j || i == n || j == n) {
return std::min(n - i, n - j);
}
int a = rk[i];
int b = rk[j];
if (a > b) {
std::swap(a, b);
}
return std::min({n - i, n - j, rmq(a, b)});
}
int lcs(int i, int j) {
if (i == j || i == 0 || j == 0) {
return std::min(i, j);
}
int a = rk[n + n - i];
int b = rk[n + n - j];
if (a > b) {
std::swap(a, b);
}
return std::min({i, j, rmq(a, b)});
}
};
// __attribute__((target("popcnt")))
void solve() {
read(int, m);
read(string, s, t);
string p = s + '#' + t;
SA sa(p);
// vector<int> pp = calc_next(p);
vector<ll> pw(5 * m + 1);
pw[0] = 1;
for (int i = 1; i <= 5 * m; ++i) {
pw[i] = pw[i - 1] * 26 % PRIME;
}
vector<int> ps = calc_z(s);
// debug(ps);
vector<int> pt = calc_z(t);
int n1 = s.size(), n2 = t.size();
for (int i = 1; i <= m; ++i) {
int tot = 2 * i + n1 + n2;
if (tot % 2) {
cout << "0 ";
continue;
}
int half = tot / 2;
int left = i;
int right = i + n1 - 1;
int l2 = i + n1 + i;
int f = 1;
if (n2 > half) {
if (pt[half] >= n2 - half) {
;;
} else {
f = 0;
}
}
// deb(n1, half, ps[half]);
if (n1 > half) {
if (ps[half] >= n1 - half) {
;;
} else {
f = 0;
}
}
int cs = max(l2 - half, left), ce = min(half - 1, right);
if (cs <= ce) {
int ds = cs + half - l2, de = ce + half - l2;
cs -= left, ce -= left;
if (sa.lcp(cs, n1 + 1 + ds) >= ce - cs + 1) {
;;
} else {
f = 0;
}
}
if (f == 0) {
cout << 0 << ' ';
continue;
}
vector<pii> segs;
segs.emplace_back(max(0, l2 - half), half - 1);
segs.emplace_back(left, min(half - 1, right));
if (right >= half) {
segs.emplace_back(0, right - half);
}
sort(segs.begin(), segs.end());
int rr = -1;
int rem = 0;
for (auto&& [l, r] : segs) {
if (l > rr) {
rem += l - rr - 1;
}
chmax(rr, r);
}
rem += half - 1 - rr;
// debug(rem);
cout << pw[rem] << ' ';
}
}
int main() {
#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
static_assert(false, "incompatible compiler variant detected.");
#endif
untie;
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t != (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
#pragma GCC optimize("Ofast,unroll-loops")
/************* This code requires C++17. ***************/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
template <typename T> struct argument_type;
template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = __float128; // up to 1e-9 precision in binary search
using pii = pair<int, int>; using pil = pair<int, ll>; using pid = pair<int, ld>;
using pli = pair<ll, int>; using pll = pair<ll, ll>; using pld = pair<ll, ld>;
using pdi = pair<ld, int>; using pdl = pair<ld, ll>; using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>; using tiil = tuple<int, int, ll>; using tiid = tuple<int, int, ld>;
using tili = tuple<int, ll, int>; using till = tuple<int, ll, ll>; using tild = tuple<int, ll, ld>;
using tidi = tuple<int, ld, int>; using tidl = tuple<int, ld, ll>; using tidd = tuple<int, ld, ld>;
using tlii = tuple<ll, int, int>; using tlil = tuple<ll, int, ll>; using tlid = tuple<ll, int, ld>;
using tlli = tuple<ll, ll, int>; using tlll = tuple<ll, ll, ll>; using tlld = tuple<ll, ll, ld>;
using tldi = tuple<ll, ld, int>; using tldl = tuple<ll, ld, ll>; using tldd = tuple<ll, ld, ld>;
using tdii = tuple<ld, int, int>; using tdil = tuple<ld, int, ll>; using tdid = tuple<ld, int, ld>;
using tdli = tuple<ld, ll, int>; using tdll = tuple<ld, ll, ll>; using tdld = tuple<ld, ll, ld>;
using tddi = tuple<ld, ld, int>; using tddl = tuple<ld, ld, ll>; using tddd = tuple<ld, ld, ld>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll PRIMELL = 901017227882342239LL;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937_64 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!((var) == (val))) (var) = (val); else
#define continue_or(var, val) __AS_PROCEDURE(if ((var) == (val)) continue; (var) = (val);)
#define break_or(var, val) __AS_PROCEDURE(if ((var) == (val)) break; (var) = (val);)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
safe_hash hasher;
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
auto h = hasher(x);
res1 = (res1 + h * pw1) % __array_hash_mdl1;
res2 = (res2 + h * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
// add declarations to avoid circular dependency
template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
template<typename T> ostream& operator<<(ostream&, const vector<T>&);
std::ostream& operator<<(std::ostream&, const int128&);
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
for (size_t i = 0; i < N; ++i) in >> a[i];
return in;
}
template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
for (auto&& i : a) out << i << ' ';
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::type>(cin), (n), (a).begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
#define deb(...) debug(make_tuple(__VA_ARGS__))
/* pops */
template <typename Container>
inline auto poptop(Container& q) {
auto ret = q.top();
q.pop();
return ret;
}
template <typename Container>
inline auto popback(Container& q) {
auto ret = q.back();
q.pop_back();
return ret;
}
template <typename Container>
inline auto popfront(Container& q) {
auto ret = q.front();
q.pop_front();
return ret;
}
/* math */
template <typename return_t>
return_t qpow(ll b, ll p) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
return_t half = qpow<return_t>(b, p / 2);
if (p % 2 == 1) return half * half * b;
else return half * half;
}
// dynamic modulus
ll qpow(ll b, ll p, ll mod) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
ll half = qpow(b, p / 2, mod);
if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
else return half * half % mod;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wparentheses"
// Accurately find `i` 'th root of `n` (taking the floor)
inline ll root(ll n, ll i) {
ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
while (l < r) {
ll mid = l + r + 1 >> 1;
if (qpow<int128>(mid, i) <= n) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
#pragma GCC diagnostic pop
#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
__attribute__((target("lzcnt")))
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
template <typename T>
T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(const string& s, const string& t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(const string& s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(int128(lhs.val) * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename T, typename U>
bool chmax(T& lhs, const U& rhs) {
bool ret = lhs < rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
template <typename T, typename U>
bool chmin(T& lhs, const U& rhs) {
bool ret = lhs > rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
#define functor(func) ([&](auto&&... val) \
noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
{return func(std::forward<decltype(val)>(val)...);})
#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
}
#define initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
namespace detail {
template <typename T, std::size_t...Is>
constexpr std::array<T, sizeof...(Is)>
make_array(const T& value, std::index_sequence<Is...>) {
return {{(static_cast<void>(Is), value)...}};
}
}
template <typename T, std::size_t N>
constexpr std::array<T, N> __initarray(const T& value) {
return detail::make_array(value, std::make_index_sequence<N>());
}
/*******************************************************/
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {
}
// __attribute__((target("popcnt")))
void solve() {
read(int, n);
vector<int> res;
int start = 1;
if (n % 8 == 1) {
res.emplace_back(1);
start = 2;
} else if (n % 8 == 2) {
res = { 1, 2 };
start = 3;
} else if (n % 8 == 3) {
res = { 1, 2, 3 };
start = 4;
} else if (n % 8 == 4) {
res = { 1, 2, 3, 4 };
start = 5;
} else if (n % 8 == 5) {
res = { 5, 2, 1, 4, 3 };
start = 6;
} else if (n % 8 == 6) {
res = { 5, 2, 3, 6, 1, 4 };
start = 7;
} else if (n % 8 == 7) {
res = { 1, 4, 7, 2, 3, 6, 5 };
start = 8;
}
for (int i = start; i + 7 <= n; i += 8) {
vector<int> curr = { i + 2, i + 7, i + 4, i + 1, i + 6, i + 3, i, i + 5 };
res.insert(res.end(), curr.begin(), curr.end());
}
putvec(res);
}
int main() {
#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
static_assert(false, "incompatible compiler variant detected.");
#endif
untie;
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t != (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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// #pragma GCC target("popcnt,lzcnt,abm,bmi,bmi2")
#pragma GCC optimize("Ofast,unroll-loops")
/************* This code requires C++17. ***************/
#include<bits/stdc++.h>
using namespace std;
/* macro helpers */
#define __NARGS(...) std::tuple_size<decltype(std::make_tuple(__VA_ARGS__))>::value
#define __DECOMPOSE_S(a, x) auto x = a;
#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a;
constexpr void __() {}
#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __()
#define __as_typeof(container) remove_reference<decltype(container)>::type
template <typename T> struct argument_type;
template <typename T, typename U> struct argument_type<T(U)> { using type = U; };
/* type aliases */
#if LONG_LONG_MAX != INT64_MAX
using ll = int64_t;
using ull = uint64_t;
#else
using ll = long long;
using ull = unsigned long long;
#endif
using int128 = __int128_t;
using uint128 = __uint128_t;
using ld = __float128; // up to 1e-9 precision in binary search
using pii = pair<int, int>; using pil = pair<int, ll>; using pid = pair<int, ld>;
using pli = pair<ll, int>; using pll = pair<ll, ll>; using pld = pair<ll, ld>;
using pdi = pair<ld, int>; using pdl = pair<ld, ll>; using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>; using tiil = tuple<int, int, ll>; using tiid = tuple<int, int, ld>;
using tili = tuple<int, ll, int>; using till = tuple<int, ll, ll>; using tild = tuple<int, ll, ld>;
using tidi = tuple<int, ld, int>; using tidl = tuple<int, ld, ll>; using tidd = tuple<int, ld, ld>;
using tlii = tuple<ll, int, int>; using tlil = tuple<ll, int, ll>; using tlid = tuple<ll, int, ld>;
using tlli = tuple<ll, ll, int>; using tlll = tuple<ll, ll, ll>; using tlld = tuple<ll, ll, ld>;
using tldi = tuple<ll, ld, int>; using tldl = tuple<ll, ld, ll>; using tldd = tuple<ll, ld, ld>;
using tdii = tuple<ld, int, int>; using tdil = tuple<ld, int, ll>; using tdid = tuple<ld, int, ld>;
using tdli = tuple<ld, ll, int>; using tdll = tuple<ld, ll, ll>; using tdld = tuple<ld, ll, ld>;
using tddi = tuple<ld, ld, int>; using tddl = tuple<ld, ld, ll>; using tddd = tuple<ld, ld, ld>;
template <typename T> using max_heap = priority_queue<T>;
template <typename T> using min_heap = priority_queue<T, vector<T>, greater<>>;
template <typename T> using oi = ostream_iterator<T>;
template <typename T> using ii = istream_iterator<T>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
constexpr ll PRIMELL = 901017227882342239LL;
constexpr ll MDL1 = 8784491;
constexpr ll MDL2 = PRIME;
constexpr int128 INT128_MAX = numeric_limits<int128>::max();
constexpr uint128 UINT128_MAX = numeric_limits<uint128>::max();
constexpr int128 INT128_MIN = numeric_limits<int128>::min();
constexpr uint128 UINT128_MIN = numeric_limits<uint128>::min();
/* random */
mt19937_64 rd(chrono::duration_cast<chrono::milliseconds>(chrono::system_clock::now().time_since_epoch()).count());
/* bit-wise operations */
#define lowbit(x) ((x) & -(x))
#define popcount(x) (__builtin_popcountll(ll(x)))
#define parity(x) (__builtin_parityll(ll(x)))
#define msp(x) (63LL - __builtin_clzll(ll(x)))
#define lsp(x) (__builtin_ctzll(ll(x)))
/* arithmetic operations */
#define mod(x, y) ((((x) % (y)) + (y)) % (y))
/* fast pairs */
#define upair ull
#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1)))
#define u1(p) ((p) >> 32)
#define u2(p) ((p) & ((1ULL << 32) - 1))
#define ult std::less<upair>
#define ugt std::greater<upair>
#define ipair ull
#define imake(x, y) (umake(x, y))
#define i1(p) (int(u1(ll(p))))
#define i2(p) (ll(u2(p) << 32) >> 32)
struct ilt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) < i2(b);
else return i1(a) < i1(b);
}
};
struct igt {
bool operator()(const ipair& a, const ipair& b) const {
if (i1(a) == i1(b)) return i2(a) > i2(b);
else return i1(a) > i1(b);
}
};
/* conditions */
#define loop while (1)
#define if_or(var, val) if (!((var) == (val))) (var) = (val); else
#define continue_or(var, val) __AS_PROCEDURE(if ((var) == (val)) continue; (var) = (val);)
#define break_or(var, val) __AS_PROCEDURE(if ((var) == (val)) break; (var) = (val);)
/* hash */
struct safe_hash {
// https://codeforces.com/blog/entry/62393
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash {
template <typename T, typename U>
size_t operator()(const pair<T, U>& a) const {
auto hash1 = safe_hash()(a.first);
auto hash2 = safe_hash()(a.second);
if (hash1 != hash2) {
return hash1 ^ hash2;
}
return hash1;
}
};
uniform_int_distribution<mt19937::result_type> dist(PRIME);
const size_t __array_hash_b = 31, __array_hash_mdl1 = dist(rd), __array_hash_mdl2 = dist(rd);
struct array_hash {
safe_hash hasher;
template <typename Sequence>
size_t operator()(const Sequence& arr) const {
size_t pw1 = 1, pw2 = 1;
size_t res1 = 0, res2 = 0;
for (auto&& x : arr) {
auto h = hasher(x);
res1 = (res1 + h * pw1) % __array_hash_mdl1;
res2 = (res2 + h * pw2) % __array_hash_mdl2;
pw1 = (pw1 * __array_hash_b) % __array_hash_mdl1;
pw2 = (pw2 * __array_hash_b) % __array_hash_mdl2;
}
return res1 + res2;
}
};
/* build data structures */
#define faster(um) __AS_PROCEDURE((um).reserve(1024); (um).max_load_factor(0.25);)
#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];)
#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];)
#define adj(ch, n) __AS_PROCEDURE(vector<vector<int>> ch((n) + 1);)
#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);)
#define edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__), ch[v].emplace_back(u, __VA_ARGS__);)
#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
#define Edgew(ch, u, v, ...) __AS_PROCEDURE(ch[u].emplace_back(v, __VA_ARGS__);)
template <typename T, typename Iterator> pair<size_t, map<T, size_t>> discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
map<T, size_t> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
template <typename T, typename Iterator> pair<size_t, unordered_map<T, size_t, safe_hash>> unordered_discretize(Iterator __first, Iterator __last) {
set<T> st(__first, __last);
size_t N = 0;
unordered_map<T, size_t, safe_hash> mp;
for (auto&& x : st) mp[x] = ++N;
return {N, mp};
}
/* io */
#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL))
// add declarations to avoid circular dependency
template<typename T, typename U> istream& operator>>(istream&, pair<T, U>&);
template<typename T, typename U> ostream& operator<<(ostream&, const pair<T, U>&);
template<typename T, size_t N> istream& operator>>(istream&, array<T, N>&);
template <typename T, size_t N> ostream& operator<<(ostream&, const array<T, N>&);
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>&, const std::tuple<Args...>&);
template<typename T> ostream& operator<<(ostream&, const vector<T>&);
std::ostream& operator<<(std::ostream&, const int128&);
template<typename T, typename U> istream& operator>>(istream& in, pair<T, U>& p) {
return in >> p.first >> p.second;
}
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
return out;
}
template<typename T, size_t N> istream& operator>>(istream& in, array<T, N>& a) {
for (size_t i = 0; i < N; ++i) in >> a[i];
return in;
}
template <typename T, size_t N> ostream& operator<<(ostream& out, const array<T, N>& a) {
for (auto&& i : a) out << i << ' ';
return out;
}
template<typename Char, typename Traits, typename Tuple, std::size_t... Index>
void print_tuple_impl(std::basic_ostream<Char, Traits>& os, const Tuple& t, std::index_sequence<Index...>) {
using swallow = int[]; // guaranties left to right order
(void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get<Index>(t)), 0)... };
}
template<typename Char, typename Traits, typename... Args>
decltype(auto) operator<<(std::basic_ostream<Char, Traits>& os, const std::tuple<Args...>& t) {
os << "{";
print_tuple_impl(os, t, std::index_sequence_for<Args...>{});
return os << "}";
}
template<typename T> ostream& operator<<(ostream& out, const vector<T>& vec) {
for (auto&& i : vec) out << i << ' ';
return out;
}
std::ostream& operator<<(std::ostream& dest, const int128& value) {
// https://stackoverflow.com/a/25115163/23881100
std::ostream::sentry s( dest );
if ( s ) {
uint128 tmp = value < 0 ? -value : value;
char buffer[ 128 ];
char* d = std::end( buffer );
do {
-- d;
*d = "0123456789"[ tmp % 10 ];
tmp /= 10;
} while ( tmp != 0 );
if ( value < 0 ) {
-- d;
*d = '-';
}
int len = std::end( buffer ) - d;
if ( dest.rdbuf()->sputn( d, len ) != len ) {
dest.setstate( std::ios_base::badbit );
}
}
return dest;
}
template<typename T> void __read(T& x) { cin >> x; }
template<typename T, typename... U> void __read(T& x, U&... args) { cin >> x; __read(args...); }
#define read(t, ...) __AS_PROCEDURE(argument_type<void(t)>::type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a(n); for (auto& x : (a)) cin >> x;)
#define readvec1(t, a, n) __AS_PROCEDURE(vector<argument_type<void(t)>::type> a((n) + 1); copy_n(ii<argument_type<void(t)>::type>(cin), (n), (a).begin() + 1);)
#define putvec(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec1(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, " ")); cout << endl;)
#define putvec_eol(a) __AS_PROCEDURE(copy((a).begin(), (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define putvec1_eol(a) __AS_PROCEDURE(copy((a).begin() + 1, (a).end(), oi<__as_typeof(a)::value_type>(cout, "\n"));)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : (a)) cerr << x << ' '; cerr << endl;)
#define deb(...) debug(make_tuple(__VA_ARGS__))
/* pops */
template <typename Container>
inline auto poptop(Container& q) {
auto ret = q.top();
q.pop();
return ret;
}
template <typename Container>
inline auto popback(Container& q) {
auto ret = q.back();
q.pop_back();
return ret;
}
template <typename Container>
inline auto popfront(Container& q) {
auto ret = q.front();
q.pop_front();
return ret;
}
/* math */
template <typename return_t>
return_t qpow(ll b, ll p) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
return_t half = qpow<return_t>(b, p / 2);
if (p % 2 == 1) return half * half * b;
else return half * half;
}
// dynamic modulus
ll qpow(ll b, ll p, ll mod) {
if (b == 0 and p != 0) return 0;
if (p == 0) return 1;
ll half = qpow(b, p / 2, mod);
if (p % 2 == 1) return (int128(half) * half % mod) * b % mod;
else return half * half % mod;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wparentheses"
// Accurately find `i` 'th root of `n` (taking the floor)
inline ll root(ll n, ll i) {
ll l = 0, r = pow(LLONG_MAX, (long double)(1) / i);
while (l < r) {
ll mid = l + r + 1 >> 1;
if (qpow<int128>(mid, i) <= n) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
#pragma GCC diagnostic pop
#define comb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] / fact[k] / fact[(n) - (k)])
#define fastcomb(n, k) ((n) < 0 or (k) < 0 or (n) < (k) ? 0 : fact[n] * factrev[k] * factrev[(n) - (k)])
__attribute__((target("lzcnt")))
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
template <typename T>
T mygcd(T a, T b) { return b == 0 ? a : mygcd(b, a % b); }
void __exgcd(ll a, ll b, ll& x, ll& y) {
if (b == 0) {
x = 1, y = 0;
return;
}
__exgcd(b, a % b, y, x);
y -= a / b * x;
}
ll inverse(ll a, ll b) {
ll x, y;
__exgcd(a, b, x, y);
return mod(x, b);
}
vector<tuple<int, int, ll>> decompose(ll x) {
// return (factor, count, factor ** count)
vector<tuple<int, int, ll>> res;
for (int i = 2; i * i <= x; i++) {
if (x % i == 0) {
int cnt = 0;
ll pw = 1;
while (x % i == 0) ++cnt, x /= i, pw *= i;
res.emplace_back(i, cnt, pw);
}
}
if (x != 1) {
res.emplace_back(x, 1, x);
}
return res;
}
vector<pii> decompose_prime(int N) {
// return (factor, count)
vector<pii> result;
for (int i = 2; i * i <= N; i++) {
if (N % i == 0) {
int cnt = 0;
while (N % i == 0) N /= i, ++cnt;
result.emplace_back(i, cnt);
}
}
if (N != 1) {
result.emplace_back(N, 1);
}
return result;
}
/* string algorithms */
vector<int> calc_next(string t) { // pi function of t
int n = (int)t.length();
vector<int> pi(n);
for (int i = 1; i < n; i++) {
int j = pi[i - 1];
while (j > 0 && t[i] != t[j]) j = pi[j - 1];
if (t[i] == t[j]) j++;
pi[i] = j;
}
return pi;
}
vector<int> calc_z(string t) { // z function of t
int m = t.length();
vector<int> z;
z.push_back(m);
pair<int, int> prev = {1, -1};
for (int i = 1; i < m; ++i) {
if (z[i - prev.first] + i <= prev.second) {
z.push_back(z[i - prev.first]);
} else {
int j = max(i, prev.second + 1);
while (j < m && t[j] == t[j - i]) ++j;
z.push_back(j - i);
prev = {i, j - 1};
}
}
return z;
}
vector<int> kmp(const string& s, const string& t) { // find all t in s
string cur = t + '#' + s;
int sz1 = s.size(), sz2 = t.size();
vector<int> v;
vector<int> lps = calc_next(cur);
for (int i = sz2 + 1; i <= sz1 + sz2; i++) {
if (lps[i] == sz2) v.push_back(i - 2 * sz2);
}
return v;
}
int period(const string& s) { // find the length of shortest recurring period
int n = s.length();
auto z = calc_z(s);
for (int i = 1; i <= n / 2; ++i) {
if (n % i == 0 && z[i] == n - i) {
return i;
}
}
return n;
}
/* modular arithmetic */
template <ll mdl> struct MLL {
ll val;
MLL(ll v = 0) : val(mod(v, mdl)) {}
MLL(const MLL<mdl>& other) : val(other.val) {}
friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); }
friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); }
friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(int128(lhs.val) * rhs.val, mdl); }
friend MLL operator/(const MLL& lhs, const MLL& rhs) { return lhs * mod(inverse(rhs.val, mdl), mdl); }
friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); }
friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; }
friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; }
MLL& operator+=(const MLL& rhs) { return *this = *this + rhs; }
MLL& operator-=(const MLL& rhs) { return *this = *this - rhs; }
MLL& operator*=(const MLL& rhs) { return *this = *this * rhs; }
MLL& operator/=(const MLL& rhs) { return *this = *this / rhs; }
MLL& operator%=(const MLL& rhs) { return *this = *this % rhs; }
};
template <ll mdl>
ostream& operator<<(ostream& out, const MLL<mdl>& num) {
return out << num.val;
}
template <ll mdl>
istream& operator>>(istream& in, MLL<mdl>& num) {
return in >> num.val;
}
// miscancellous
template <typename T, typename U>
bool chmax(T& lhs, const U& rhs) {
bool ret = lhs < rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
template <typename T, typename U>
bool chmin(T& lhs, const U& rhs) {
bool ret = lhs > rhs;
if (ret) {
lhs = rhs;
}
return ret;
}
#define functor(func) ([&](auto&&... val) \
noexcept(noexcept(func(std::forward<decltype(val)>(val)...))) -> decltype(auto) \
{return func(std::forward<decltype(val)>(val)...);})
#define expr(ret, ...) ([&] (__VA_ARGS__) { return (ret); })
template <typename Func, typename RandomIt> void sort_by_key(RandomIt first, RandomIt last, Func extractor) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return std::less<>()(extractor(a), extractor(b)); });
}
template <typename Func, typename RandomIt, typename Compare> void sort_by_key(RandomIt first, RandomIt last, Func extractor, Compare comp) {
std::sort(first, last, [&] (auto&& a, auto&& b) { return comp(extractor(a), extractor(b)); });
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip(Iterator_T a_first, Iterator_T a_last, Iterator_U b_first, Iterator_U b_last) {
vector<pair<T, U>> res;
auto a_it = a_first;
auto b_it = b_first;
for (; not (a_it == a_last) and not (b_it == b_last); ++a_it, ++b_it) {
res.emplace_back(*a_it, *b_it);
}
return res;
}
template <typename T, typename U, typename Iterator_T, typename Iterator_U>
vector<pair<T, U>> zip_n(Iterator_T a_first, Iterator_U b_first, size_t n) {
vector<pair<T, U>> res;
if (n > 0) {
res.emplace_back(*a_first, *b_first);
for (size_t i = 1; i != n; ++i) {
res.emplace_back(*++a_first, *++b_first);
}
}
return res;
}
template <typename T>
class ArithmeticIterator : bidirectional_iterator_tag {
public:
using difference_type = ptrdiff_t;
using value_type = T;
private:
value_type value;
public:
ArithmeticIterator(const T& value) : value(value) {}
value_type operator*() const { return value; }
ArithmeticIterator<T>& operator++() { ++value; return *this; }
ArithmeticIterator<T>& operator--() { --value; return *this; }
bool operator==(const ArithmeticIterator<T>& rhs) const { return value == rhs.value; }
};
template <typename T> vector<pair<int, T>> enumerate(const vector<T>& container) {
return zip<int, T>(ArithmeticIterator<int>(0), ArithmeticIterator<int>(INT_MAX), container.begin(), container.end());
}
#define initarray(init, N) (__initarray<decay<decltype(init)>::type, (N)>(init))
namespace detail {
template <typename T, std::size_t...Is>
constexpr std::array<T, sizeof...(Is)>
make_array(const T& value, std::index_sequence<Is...>) {
return {{(static_cast<void>(Is), value)...}};
}
}
template <typename T, std::size_t N>
constexpr std::array<T, N> __initarray(const T& value) {
return detail::make_array(value, std::make_index_sequence<N>());
}
/*******************************************************/
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define TOT_TEST_CASE 10000
void dump() {}
void dump_ignore() {}
void prep() {
}
template<typename T>
struct BIT {
int n;
vector<T> c;
BIT(size_t n) : n(n), c(n + 1) {}
void add(size_t i, const T& k) {
while (i <= n) {
c[i] += k;
i += lowbit(i);
}
}
T getsum(size_t i) {
T res = {};
while (i) {
res += c[i];
i -= lowbit(i);
}
return res;
}
};
// __attribute__((target("popcnt")))
void solve() {
read(int, n, m);
vector a(n, vector<int>(m));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
cin >> a[i][j];
}
}
vector<pii> rows;
vector<vector<int>> cols;
bool row_sorted = 1, col_sorted = 1;
int prev_mx = -1;
for (int i = 0; i < n; ++i) {
int mn = INF, mx = -INF;
for (int j = 0; j < m; ++j) {
chmin(mn, a[i][j]);
chmax(mx, a[i][j]);
}
vector<int> idx(m);
iota(idx.begin(), idx.end(), 0);
sort_by_key(idx.begin(), idx.end(), expr(a[i][j], auto&& j));
cols.emplace_back(idx);
rows.emplace_back(mn, mx);
if (mn > prev_mx) {
;;
} else {
row_sorted = 0;
}
prev_mx = mx;
}
for (int i = 1; i < m; ++i) {
if (cols[0][i] > cols[0][i - 1]) {
;;
} else {
col_sorted = 0;
}
}
vector<int> rowidx(n), colidx(m);
iota(rowidx.begin(), rowidx.end(), 0);
iota(colidx.begin(), colidx.end(), 0);
sort_by_key(rowidx.begin(), rowidx.end(), expr(rows[i], auto i));
sort_by_key(colidx.begin(), colidx.end(), expr(a[0][i], auto i));
for (int i = 1; i < n; ++i) {
if (rows[rowidx[i]].first < rows[rowidx[i - 1]].second or cols[rowidx[i]] != cols[rowidx[i - 1]]) {
cout << "NSFW\n";
return;
}
}
int rowinv = 0, colinv = 0;
{
vector<bool> vis(n);
int cnt;
{
auto dfs = [&] (auto dfs, int v) -> void {
vis[v] = 1;
cnt += 1;
if (not vis[rowidx[v]]) dfs(dfs, rowidx[v]);
};
for (int i = 0; i < n; ++i) {
if (not vis[i]) {
cnt = 0;
dfs(dfs, i);
rowinv += cnt - 1;
}
}
}
}
{
vector<bool> vis(m);
int cnt;
{
auto dfs = [&] (auto dfs, int v) -> void {
vis[v] = 1;
cnt += 1;
if (not vis[colidx[v]]) dfs(dfs, colidx[v]);
};
for (int i = 0; i < m; ++i) {
if (not vis[i]) {
cnt = 0;
dfs(dfs, i);
colinv += cnt - 1;
}
}
}
}
if (rowinv % 2 == colinv % 2) {
// fox loses
if (n == 2) {
cout << "CAT\n";
} else {
cout << "NSFW\n";
}
} else {
// cat loses
if (m == 2 or rowinv == 1 and colinv == 0) {
cout << "FOX\n";
} else {
cout << "NSFW\n";
}
}
}
int main() {
#if __cplusplus < 201402L or defined(_MSC_VER) and not defined(__clang__)
static_assert(false, "incompatible compiler variant detected.");
#endif
untie;
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t != (TOT_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

View File

@ -1,7 +1,4 @@
5 2 3
2 4
4 3
4 2
4 1
2 5
6
bbabbababbab
bab

View File

@ -8,10 +8,12 @@ import io
PRIME = 998_244_353
if __name__ == '__main__':
N = 100000
M = N // 2
print(N, M, N)
for i in range(1, M + 1):
print(randint(1, 2 * i - 1), 2 * i)
for _ in range(N):
print(randint(1, N), randint(1, N))
res = 0
N = 75
for i in range(N):
for j in range(i + 1, N):
for k in range(0, j - i + 1 + 1):
for l in range(0, j - i + 1 - k + 1):
for m in range(0, (j - i + 1) // 2 + 1):
res += 1
print(res)