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subcrip 2024-04-26 16:40:06 +08:00
parent 2b2be9dd19
commit 85ce97a752
Signed by: subcrip
SSH Key Fingerprint: SHA256:dFPFi68d8C87YkFkEBU4TkcrYRySWpekRR1hbnDWUCw
13 changed files with 3599 additions and 111 deletions

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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 {
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) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * 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 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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
private:
using size_type = uint64_t;
using info_type = Addable_Info_t;
using tag_type = Tag_t;
size_type _max;
vector<info_type> d;
vector<tag_type> b;
void pull(size_type p) {
d[p] = d[p * 2] + d[p * 2 + 1];
}
void push(size_type p, size_type left_len, size_type right_len) {
d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
b[p] = tag_type();
}
void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
if (s == t) {
d[p] = c;
return;
}
size_type m = s + (t - s >> 1);
if (s != t) push(p, m - s + 1, t - m);
if (x <= m) set(s, m, p * 2, x, c);
else set(m + 1, t, p * 2 + 1, x, c);
d[p] = d[p * 2] + d[p * 2 + 1];
}
void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
if (l <= s && t <= r) {
d[p].apply(c, t - s + 1);
b[p].apply(c);
return;
}
size_type m = s + (t - s >> 1);
push(p, m - s + 1, t - m);
if (l <= m) range_apply(s, m, p * 2, l, r, c);
if (r > m) range_apply(m + 1, t, p * 2 + 1, l, r, c);
pull(p);
}
info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
if (l <= s && t <= r) {
return d[p];
}
size_type m = s + (t - s >> 1);
info_type res = {};
push(p, m - s + 1, t - m);
if (l <= m) res = res + range_query(s, m, p * 2, l, r);
if (r > m) res = res + range_query(m + 1, t, p * 2 + 1, l, r);
return res;
}
void build(const Sequence& a, size_type s, size_type t, size_type p) {
if (s == t) {
d[p] = a[s];
return;
}
int m = s + (t - s >> 1);
build(a, s, m, p * 2);
build(a, m + 1, t, p * 2 + 1);
pull(p);
}
public:
segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
segtree(const Sequence& a) : segtree(a.size()) {
build(a, {}, _max, 1);
}
void set(size_type i, const info_type& c) {
set({}, _max, 1, i, c);
}
void range_apply(size_type l, size_type r, const tag_type& c) {
range_apply({}, _max, 1, l, r, c);
}
void apply(size_type i, const tag_type& c) {
range_apply(i, i, c);
}
info_type range_query(size_type l, size_type r) {
return range_query({}, _max, 1, l, r);
}
info_type query(size_type i) {
return range_query(i, i);
}
Sequence serialize() {
Sequence res = {};
for (size_type i = 0; i <= _max; ++i) {
res.push_back(query(i));
}
return res;
}
const vector<info_type>& get_d() {
return d;
}
};
struct Tag {
int val = INT_MIN;
void apply(const Tag& rhs) {
if (rhs.val != -1)
val = rhs.val;
}
};
struct Info {
int val = INT_MIN;
void apply(const Tag& rhs, size_t len) {
val = max(val, rhs.val);
}
};
Info operator+(const Info &a, const Info &b) {
return {max(a.val, b.val)};
}
void solve() {
read(int, n);
readvec(int, a, n);
vector<ll> ps(n + 1);
for (int i = 1; i <= n; ++i) {
ps[i] = ps[i - 1] + a[i - 1];
}
set<ll> st(ps.begin(), ps.end());
unordered_map<ll, int, safe_hash> mp;
int N = 0;
for (auto&& x : st) mp[x] = ++N;
// for (int i = 0; i <= n; ++i) {
// cerr << mp[ps[i]] << " \n"[i == n];
// }
// for (auto&& [x, y] : mp) cerr << x << ' ' << y << '\n';
segtree<Info, Tag> dp(N + 1);
dp.set(mp[0], {0});
int prev = 0;
for (int i = 1; i <= n; ++i) {
int curr = max(prev, dp.range_query(0, mp[ps[i]]).val + i);
// debug(curr);
dp.apply(mp[ps[i]], { curr - i });;
prev = curr;
}
// for (auto&& x : dp.serialize()) cerr << x.val << ' ';
// cerr << endl;
cout << prev << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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 {
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) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * 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 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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n);
vector<int> a(n), b(n);
int first_one = -1;
for (int i = 0; i < n; ++i) {
read(char, c);
a[i] = c - 48;
if (first_one == -1 and a[i]) {
first_one = i;
}
}
for (int i = 0; i < n; ++i) {
read(char, c);
b[i] = c - 48;
}
vector<int> seq;
auto apply = [&] (int op) {
seq.emplace_back(op);
vector<int> curr(n);
for (int j = 0; j < n; ++j) {
if (j + op >= 0 and j + op < n) {
curr[j] = a[j + op];
}
}
for (int j = 0; j < n; ++j) {
a[j] ^= curr[j];
}
};
if (first_one != -1) {
int start = 0;
while (start < n) {
if (a[start] or b[start]) {
break;
}
++start;
}
if (start != n) {
if (a[start] == 0 and b[start] == 1) {
int next_one = -1;
for (int i = start + 1; i < n; ++i) {
if (a[i] == 1) {
next_one = i;
break;
}
}
if (next_one != -1) {
apply(next_one - start);
first_one = start;
} else {
cout << -1 << '\n';
return;
}
} else {
first_one = start;
}
} else {
cout << 0 << '\n';
return;
}
for (int i = start + 1; i < n; ++i) {
if (a[i] != b[i]) {
apply(first_one - i);
}
}
while (first_one != -1 and a[first_one] != b[first_one]) {
int last_one = -1;
for (int i = n - 1; i > first_one; --i) {
if (a[i]) {
last_one = i;
break;
}
}
if (last_one != -1) {
apply(last_one - first_one);
int new_first_one = -1;
for (int i = first_one - 1; i >= 0; --i) {
if (a[i]) {
new_first_one = i;
break;
}
}
first_one = new_first_one;
} else {
cout << -1 << '\n';
return;
}
}
}
// debug(a), debug(b);;
for (int i = 0; i < n; ++i) {
if (a[i] != b[i]) {
cout << -1 << '\n';
return;
}
}
cout << seq.size() << '\n';
if (seq.size()) {
putvec(seq);
}
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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src/bin/cf-1799d2.cc Normal file
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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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 {
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) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * 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 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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
private:
using size_type = uint64_t;
using info_type = Addable_Info_t;
using tag_type = Tag_t;
size_type _max;
vector<info_type> d;
vector<tag_type> b;
void pull(size_type p) {
d[p] = d[p * 2] + d[p * 2 + 1];
}
void push(size_type p, size_type left_len, size_type right_len) {
d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
b[p] = tag_type();
}
void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
if (s == t) {
d[p] = c;
return;
}
size_type m = s + (t - s >> 1);
if (s != t) push(p, m - s + 1, t - m);
if (x <= m) set(s, m, p * 2, x, c);
else set(m + 1, t, p * 2 + 1, x, c);
d[p] = d[p * 2] + d[p * 2 + 1];
}
void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
if (l <= s && t <= r) {
d[p].apply(c, t - s + 1);
b[p].apply(c);
return;
}
size_type m = s + (t - s >> 1);
push(p, m - s + 1, t - m);
if (l <= m) range_apply(s, m, p * 2, l, r, c);
if (r > m) range_apply(m + 1, t, p * 2 + 1, l, r, c);
pull(p);
}
info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
if (l <= s && t <= r) {
return d[p];
}
size_type m = s + (t - s >> 1);
info_type res = {};
push(p, m - s + 1, t - m);
if (l <= m) res = res + range_query(s, m, p * 2, l, r);
if (r > m) res = res + range_query(m + 1, t, p * 2 + 1, l, r);
return res;
}
void build(const Sequence& a, size_type s, size_type t, size_type p) {
if (s == t) {
d[p] = a[s];
return;
}
int m = s + (t - s >> 1);
build(a, s, m, p * 2);
build(a, m + 1, t, p * 2 + 1);
pull(p);
}
public:
segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
segtree(const Sequence& a) : segtree(a.size()) {
build(a, {}, _max, 1);
}
void set(size_type i, const info_type& c) {
set({}, _max, 1, i, c);
}
void range_apply(size_type l, size_type r, const tag_type& c) {
range_apply({}, _max, 1, l, r, c);
}
void apply(size_type i, const tag_type& c) {
range_apply(i, i, c);
}
info_type range_query(size_type l, size_type r) {
return range_query({}, _max, 1, l, r);
}
info_type query(size_type i) {
return range_query(i, i);
}
Sequence serialize() {
Sequence res = {};
for (size_type i = 0; i <= _max; ++i) {
res.push_back(query(i));
}
return res;
}
const vector<info_type>& get_d() {
return d;
}
};
struct Tag {
ll val = 0;
void apply(const Tag& rhs) {
val += rhs.val;
}
};
struct Info {
ll val = LLONG_MAX;
void apply(const Tag& rhs, size_t len) {
if (rhs.val < 0 or val <= LLONG_MAX - rhs.val) {
val += rhs.val;
} else {
val = LLONG_MAX;
}
}
};
Info operator+(const Info &a, const Info &b) {
return {min(a.val, b.val)};
}
void solve() {
read(int, n, k);
readvec(int, idx, n);
readvec(int, a, k);
readvec(int, b, k);
segtree<Info, Tag> row(k + 1), col(k + 1);
// vector<bool> row_enable(k + 1), col_enable(k + 1);
row.set(0, {0});
col.set(0, {0});
int prev = 0;
for (auto&& i : idx) {
if (i == prev) {
row.range_apply(0, k, {b[i - 1]});
col.range_apply(0, k, {b[i - 1]});
} else {
ll row_query = row.query(i).val;
ll col_query = col.query(i).val;
ll prev_row = min(row.range_query(0, k).val + a[i - 1], row_query != LLONG_MAX ? row_query + b[i - 1] : LLONG_MAX);
ll prev_col = min(col.range_query(0, k).val + a[i - 1], col_query != LLONG_MAX ? col_query + b[i - 1] : LLONG_MAX);
row.range_apply(0, k, {a[i - 1]});
col.range_apply(0, k, {a[i - 1]});
row.apply(i, {b[i - 1] - a[i - 1]});
col.apply(i, {b[i - 1] - a[i - 1]});
row.set(prev, {prev_col});
col.set(prev, {prev_row});
// for (auto&& x : row.serialize()) {
// cerr << x.val << ' ';;
// }
// cerr << endl;
// for (auto&& x : col.serialize()) {
// cerr << x.val << ' ';;
// }
// cerr << endl;
}
prev = i;
}
cout << min(row.range_query(0, k).val, col.range_query(0, k).val) << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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 {
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) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * 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 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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
unordered_map<int, int, safe_hash> st[26];
void solve() {
read(int, n);
readvec(string, a, n);
ll res = 0;
for (auto&& s : a) {
int not_mask = (1 << 26) - 1;
int curr = 0;
for (auto&& c : s) {
int x = c - 'a';
if ((not_mask >> x) & 1) {
not_mask ^= 1 << x;
}
curr ^= 1 << x;
}
int other = 0;
for (int i = 0; i < 26; ++i) {
if ((not_mask >> i) & 1) {
other |= 1 << i;
} else {
other |= (1 << i) ^ (curr & (1 << i));
}
}
for (int i = 0; i < 26; ++i) {
if ((not_mask >> i) & 1) {
res += st[i][other];
}
}
for (int i = 0; i < 26; ++i) {
if ((not_mask >> i) & 1) {
st[i][curr | 1 << i] += 1;
}
}
}
cout << res << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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;
}
};
/* build data structures */
#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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
private:
using size_type = uint64_t;
using info_type = Addable_Info_t;
using tag_type = Tag_t;
size_type _max;
vector<info_type> d;
vector<tag_type> b;
void pull(size_type p) {
d[p] = d[p * 2] + d[p * 2 + 1];
}
void push(size_type p, size_type left_len, size_type right_len) {
d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
b[p] = tag_type();
}
void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
if (s == t) {
d[p] = c;
return;
}
size_type m = s + (t - s >> 1);
if (s != t) push(p, m - s + 1, t - m);
if (x <= m) set(s, m, p * 2, x, c);
else set(m + 1, t, p * 2 + 1, x, c);
d[p] = d[p * 2] + d[p * 2 + 1];
}
void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
if (l <= s && t <= r) {
d[p].apply(c, t - s + 1);
b[p].apply(c);
return;
}
size_type m = s + (t - s >> 1);
push(p, m - s + 1, t - m);
if (l <= m) range_apply(s, m, p * 2, l, r, c);
if (r > m) range_apply(m + 1, t, p * 2 + 1, l, r, c);
pull(p);
}
info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
if (l <= s && t <= r) {
return d[p];
}
size_type m = s + (t - s >> 1);
info_type res = {};
push(p, m - s + 1, t - m);
if (l <= m) res = res + range_query(s, m, p * 2, l, r);
if (r > m) res = res + range_query(m + 1, t, p * 2 + 1, l, r);
return res;
}
void build(const Sequence& a, size_type s, size_type t, size_type p) {
if (s == t) {
d[p] = a[s];
return;
}
int m = s + (t - s >> 1);
build(a, s, m, p * 2);
build(a, m + 1, t, p * 2 + 1);
pull(p);
}
public:
segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
segtree(const Sequence& a) : segtree(a.size()) {
build(a, {}, _max, 1);
}
void set(size_type i, const info_type& c) {
set({}, _max, 1, i, c);
}
void range_apply(size_type l, size_type r, const tag_type& c) {
range_apply({}, _max, 1, l, r, c);
}
void apply(size_type i, const tag_type& c) {
range_apply(i, i, c);
}
info_type range_query(size_type l, size_type r) {
return range_query({}, _max, 1, l, r);
}
info_type query(size_type i) {
return range_query(i, i);
}
Sequence serialize() {
Sequence res = {};
for (size_type i = 0; i <= _max; ++i) {
res.push_back(query(i));
}
return res;
}
const vector<info_type>& get_d() {
return d;
}
};
struct Tag {
int val = -1;
void apply(const Tag& rhs) {
if (rhs.val != -1)
val = rhs.val;
}
};
struct Info {
int val = 0;
void apply(const Tag& rhs, size_t len) {
if (rhs.val != -1)
val = rhs.val * len;
}
};
Info operator+(const Info &a, const Info &b) {
return {max(a.val, b.val)};
}
void solve() {
read(int, n);
vector<pair<int, vector<int>>> data;
for (int i = 0; i < n; ++i) {
vector<int> curr;
read(int, k);
while (k--) {
read(int, x);
curr.emplace_back(x);
}
data.emplace_back(*max_element(curr.begin(), curr.end()), curr);
}
sort(data.begin(), data.end());
segtree<Info, Tag> dp(n + 1);
for (int i = 1; i <= n; ++i) {
auto&& curr = data[i - 1].second;
int k = curr.size();
vector<pii> st;
for (int j = k - 1; ~j; --j) {
int curr_res = 0;
while (st.size() and st.back().first <= curr[j]) {
st.pop_back();
}
// binary search for max[t] < a[j], select max(dp[t])
{
int l = 0, r = i - 1;
while (l < r) {
int mid = l + r + 1 >> 1;
if (data[mid].first >= curr[j]) {
r = mid - 1;
} else {
l = mid;
}
}
if (data[l].first < curr[j]) {
// debug(i), debug(j), debug(l), debug(dp.range_query(0, l).val), debug(st.size());
curr_res = dp.range_query(1, l + 1).val + int(st.size()) + 1;
} else {
curr_res = int(st.size()) + 1;
}
}
st.emplace_back(curr[j], curr_res);
}
dp.set(i, { max_element(st.begin(), st.end(), [] (const pii& a, const pii& b) { return a.second < b.second; })->second });
// for (auto&& x : dp.serialize()) {
// cerr << x.val << ' ';
// }
}
cout << dp.range_query(0, n).val << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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;
}
};
/* build data structures */
#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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n, m, p);
vector<vector<pii>> e(n + 1);
vector<int> w(n + 1);
for (int i = 1; i <= n; ++i) cin >> w[i];
while (m--) {
read(int, u, v, s);
e[u].emplace_back(v, s);
}
vector<pll> res(n + 1, {INFLL, 0});
res[1] = {0, p};
vector<int> idx(n);
iota(idx.begin(), idx.end(), 1);
sort(idx.begin(), idx.end(), [&] (int i, int j) { return w[i] < w[j]; });
for (auto&& i : idx) {
auto [curr_times, curr_bal] = res[i];
priority_queue<pli, vector<pli>, greater<>> pq;
vector<bool> vis(n + 1);
vector<ll> dis(n + 1, INFLL);
pq.emplace(0, i);
while (pq.size()) {
poptop(pq, d, v);
continue_or(vis[v], 1);
for (auto&& [u, w] : e[v]) {
if (d + w < dis[u]) {
dis[u] = d + w;
pq.emplace(dis[u], u);
}
}
}
for (int j = 1; j <= n; ++j) {
if (dis[j] == INFLL) continue;
ll new_times = (max(ll(0), dis[j] - curr_bal) + w[i] - 1) / w[i];
ll times = curr_times + new_times;
ll bal = curr_bal + new_times * w[i] - dis[j];
if (times < res[j].first or times == res[j].first and bal > res[j].second) {
res[j] = {times, bal};
}
}
}
cout << (res[n].first == INFLL ? -1 : res[n].first) << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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;
}
};
/* build data structures */
#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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n, q);
unordered_map<pii, ll, pair_hash> dp;
vector<int> father(n + 1);
vector<ll> a(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> a[i];
}
for (int i = 2; i <= n; ++i) {
cin >> father[i];
}
auto dfs = [&] (auto dfs, int u, int v) -> ll {
if (u == 0 and v == 0) {
return 0;
}
if (not dp.count({u, v})) dp[{u, v}] = a[u] * a[v] + dfs(dfs, father[u], father[v]);
return dp[{u, v}];
};
while (q--) {
read(int, u, v);
ll ans = dfs(dfs, u, v);
cout << ans << '\n';
}
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

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#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#endif
/////////////////////////////////////////////////////////
/**
* Useful Macros
* by subcrip
* (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) decltype(container)::value_type
/* 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 pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
/* constants */
constexpr int INF = 0x3f3f3f3f;
constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL;
constexpr ll MDL = 1e9 + 7;
constexpr ll PRIME = 998'244'353;
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 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;
}
};
/* build data structures */
#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 pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);)
#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};)
#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 Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);)
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))
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(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);)
#define readvec(type, a, n) __AS_PROCEDURE(vector<type> a(n); for (int i = 0; i < (n); ++i) cin >> a[i];)
#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;)
#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;)
#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;)
template<typename T, typename U> ostream& operator<<(ostream& out, const pair<T, U>& p) {
out << "{" << p.first << ", " << p.second << "}";
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;
}
/* pops */
#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();)
#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();)
#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();)
/* math */
constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); }
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) {
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;
}
/* 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(string s, 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(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;
}
/////////////////////////////////////////////////////////
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
void dump_ignore() {}
void prep() {}
void solve() {
read(int, n, k);
readvec(int, a, n);
array<int, int(2e5 + 10)> cnt {};
int j = 0;
int l = 2; // [j, l)
ll res = 0;
cnt[a[j]] = 1;
for (int i = 0; i < n; i += 2) {
while (j < i or i - (k - (j - i + 1)) / 2 < 0) {
cnt[a[j]] -= 1;
j += 2;
}
while (j - 2 >= i and i - (k - (j - 2 - i + 1)) / 2 >= 0) {
j -= 2;
cnt[a[j]] += 1;
}
while (l < n and l - i + 1 <= k and (l <= j or l + (k - (l - i + 1)) / 2 < n)) {
cnt[a[l]] += 1;
l += 2;
}
while (l - 2 - i + 1 > k or (l - 2 > j and l - 2 + (k - (l - 2 - i + 1)) / 2 >= n)) {
l -= 2;
cnt[a[l]] -= 1;
}
if (l <= j) {
;;
} else {
// debug(i), debug(j), debug(l);
// debug((l - j) / 2 - cnt[a[i]]);
res += (l - j) / 2 - cnt[a[i]];
}
}
if (n == 1) goto fi;
j = 1, l = 3;
cnt.fill(0);
cnt[a[j]] = 1;
for (int i = 1; i < n; i += 2) {
while (j < i or i - (k - (j - i + 1)) / 2 < 0) {
cnt[a[j]] -= 1;
j += 2;
}
while (j - 2 >= i and i - (k - (j - 2 - i + 1)) / 2 >= 0) {
j -= 2;
cnt[a[j]] += 1;
}
while (l < n and l - i + 1 <= k and (l <= j or l + (k - (l - i + 1)) / 2 < n)) {
cnt[a[l]] += 1;
l += 2;
}
while (l - 2 - i + 1 > k or (l - 2 > j and l - 2 + (k - (l - 2 - i + 1)) / 2 >= n)) {
l -= 2;
cnt[a[l]] -= 1;
}
if (l <= j) {
;;
} else {
// debug(i), debug(j), debug(l);
// debug((l - j) / 2 - cnt[a[i]]);
res += (l - j) / 2 - cnt[a[i]];
}
}
fi:
cout << res << '\n';
}
int main() {
#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__)
assert(false && "incompatible compiler variant detected.");
#endif
untie, cout.tie(NULL);
prep();
#ifdef SINGLE_TEST_CASE
solve();
#else
read(int, t);
for (int i = 0; i < t; ++i) {
#ifdef DUMP_TEST_CASE
if (t < (DUMP_TEST_CASE)) {
solve();
} else if (i + 1 == (DUMP_TEST_CASE)) {
dump();
} else {
dump_ignore();
}
#else
solve();
#endif
}
#endif
}

View File

@ -286,7 +286,7 @@ int period(string s) { // find the length of shortest recurring period
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
// #define DUMP_TEST_CASE 1431
void dump() {}
@ -309,6 +309,7 @@ public:
}
void merge(size_t i, size_t j) {
if (connected(i, j)) return;
sz[query(j)] += sz[query(i)];
c[query(i)] = query(j);
}
@ -324,36 +325,44 @@ public:
void solve() {
read(int, n, m);
adj(cand, n);
adj(ch, n);
vector<int> a(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> a[i];
}
while (m--) {
read(int, u, v);
edge(cand, u, v);
edge(ch, u, v);
}
vector<int> idx(n + 1);
quick_union qu(n + 1);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin() + 1, idx.end(), [&] (int u, int v) { return a[u] < a[v]; });
vector<bool> enable(n + 1);
for (int i = 1; i <= n; ++i) {
for (auto&& j : ch[i]) {
if (a[i] == a[j]) {
qu.merge(i, j);
}
}
}
for (int t = 1; t <= n; ++t) {
int v = idx[t];
int rest = a[v];
int mx = 0;
// debug(v), debug(rest);
for (auto&& u : cand[v]) {
if (a[u] > rest or qu.query_size(u) == 1 and a[u]) {
for (auto&& u : ch[v]) {
if (not enable[qu.query(u)]) {
continue;
}
mx = max(mx, int(qu.query_size(u)));
}
if (mx >= rest) {
for (auto&& u : cand[v]) {
if (a[u] > rest or qu.connected(u, v)) {
continue;
}
// debug(curr_sz), debug(my_sz);
enable[qu.query(v)] = 1;
}
for (auto&& u : ch[v]) {
if (a[u] < rest) {
enable[qu.query(u)] = enable[qu.query(v)];
qu.merge(v, u);
}
}
@ -361,9 +370,8 @@ void solve() {
}
int mx = 0;
for (int i = 1; i <= n; ++i) {
int sz = qu.query_size(i);
if (not (sz == 1 and a[i])) {
mx = max(mx, sz);
if (enable[qu.query(i)]) {
mx = max(mx, int( qu.query_size(i) ));
}
}
if (mx == n) {

View File

@ -120,6 +120,23 @@ struct pair_hash {
}
};
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 {
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) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * 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 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];)
@ -285,7 +302,7 @@ int period(string s) { // find the length of shortest recurring period
}
/////////////////////////////////////////////////////////
// #define SINGLE_TEST_CASE
#define SINGLE_TEST_CASE
// #define DUMP_TEST_CASE 7219
void dump() {}
@ -294,83 +311,157 @@ void dump_ignore() {}
void prep() {}
class quick_union {
template<typename Addable_Info_t, typename Tag_t, typename Sequence = std::vector<Addable_Info_t>> class segtree {
private:
vector<size_t> c, sz;
using size_type = uint64_t;
using info_type = Addable_Info_t;
using tag_type = Tag_t;
size_type _max;
vector<info_type> d;
vector<tag_type> b;
void pull(size_type p) {
d[p] = d[p * 2] + d[p * 2 + 1];
}
void push(size_type p, size_type left_len, size_type right_len) {
d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len);
b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]);
b[p] = tag_type();
}
void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) {
if (s == t) {
d[p] = c;
return;
}
size_type m = s + (t - s >> 1);
if (s != t) push(p, m - s + 1, t - m);
if (x <= m) set(s, m, p * 2, x, c);
else set(m + 1, t, p * 2 + 1, x, c);
d[p] = d[p * 2] + d[p * 2 + 1];
}
void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
if (l <= s && t <= r) {
d[p].apply(c, t - s + 1);
b[p].apply(c);
return;
}
size_type m = s + (t - s >> 1);
push(p, m - s + 1, t - m);
if (l <= m) range_apply(s, m, p * 2, l, r, c);
if (r > m) range_apply(m + 1, t, p * 2 + 1, l, r, c);
pull(p);
}
info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) {
if (l <= s && t <= r) {
return d[p];
}
size_type m = s + (t - s >> 1);
info_type res = {};
push(p, m - s + 1, t - m);
if (l <= m) res = res + range_query(s, m, p * 2, l, r);
if (r > m) res = res + range_query(m + 1, t, p * 2 + 1, l, r);
return res;
}
void build(const Sequence& a, size_type s, size_type t, size_type p) {
if (s == t) {
d[p] = a[s];
return;
}
int m = s + (t - s >> 1);
build(a, s, m, p * 2);
build(a, m + 1, t, p * 2 + 1);
pull(p);
}
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) {
sz[query(j)] += sz[query(i)];
c[query(i)] = query(j);
segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {}
segtree(const Sequence& a) : segtree(a.size()) {
build(a, {}, _max, 1);
}
bool connected(size_t i, size_t j) {
return query(i) == query(j);
void set(size_type i, const info_type& c) {
set({}, _max, 1, i, c);
}
void range_apply(size_type l, size_type r, const tag_type& c) {
range_apply({}, _max, 1, l, r, c);
}
size_t query_size(size_t i) {
return sz[query(i)];
void apply(size_type i, const tag_type& c) {
range_apply(i, i, c);
}
info_type range_query(size_type l, size_type r) {
return range_query({}, _max, 1, l, r);
}
info_type query(size_type i) {
return range_query(i, i);
}
Sequence serialize() {
Sequence res = {};
for (size_type i = 0; i <= _max; ++i) {
res.push_back(query(i));
}
return res;
}
const vector<info_type>& get_d() {
return d;
}
};
struct Tag {
int val = INT_MIN;
void apply(const Tag& rhs) {
if (rhs.val != -1)
val = rhs.val;
}
};
struct Info {
int val = INT_MIN;
void apply(const Tag& rhs, size_t len) {
val = max(val, rhs.val);
}
};
Info operator+(const Info &a, const Info &b) {
return {max(a.val, b.val)};
}
void solve() {
read(int, n, m);
adj(cand, n);
vector<int> a(n + 1);
read(int, n);
readvec(int, a, n);
vector<ll> ps(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> a[i];
ps[i] = ps[i - 1] + a[i - 1];
}
while (m--) {
read(int, u, v);
edge(cand, u, v);
}
vector<int> idx(n + 1);
quick_union qu(n + 1);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin() + 1, idx.end(), [&] (int u, int v) { return a[u] < a[v]; });
for (int t = 1; t <= n; ++t) {
int v = idx[t];
int rest = a[v];
int mx = 0;
// debug(v), debug(rest);
for (auto&& u : cand[v]) {
if (a[u] > rest or qu.query_size(u) == 1 and a[u]) {
continue;
}
mx = max(mx, int(qu.query_size(u)));
}
if (mx >= rest) {
for (auto&& u : cand[v]) {
if (a[u] > rest or qu.connected(u, v)) {
continue;
}
// debug(curr_sz), debug(my_sz);
qu.merge(v, u);
}
}
// debug(sz);
}
int mx = 0;
set<ll> st(ps.begin(), ps.end());
unordered_map<ll, int, safe_hash> mp;
int N = 0;
for (auto&& x : st) mp[x] = ++N;
// for (int i = 0; i <= n; ++i) {
// cerr << mp[ps[i]] << " \n"[i == n];
// }
// for (auto&& [x, y] : mp) cerr << x << ' ' << y << '\n';
segtree<Info, Tag> dp(N + 1);
dp.set(mp[0], {0});
int prev = 0;
for (int i = 1; i <= n; ++i) {
int sz = qu.query_size(i);
if (not (sz == 1 and a[i])) {
mx = max(mx, sz);
}
}
if (mx == n) {
cout << "YES\n";
} else {
cout << "NO\n";
int curr = max(prev, dp.range_query(0, mp[ps[i]]).val + i);
// debug(curr);
dp.apply(mp[ps[i]], { curr - i });;
prev = curr;
}
// for (auto&& x : dp.serialize()) cerr << x.val << ' ';
// cerr << endl;
cout << prev << '\n';
}
int main() {

View File

@ -1,35 +1,3 @@
5
4 3
2 1 0 3
1 2
2 3
3 4
6 6
0 1 2 3 0 1
1 2
2 3
3 4
4 5
4 6
5 6
4 3
0 1 2 0
1 2
2 3
1 3
4 6
1 1 1 0
1 2
3 2
4 3
2 4
4 1
1 3
5 5
0 1 3 2 0
1 2
2 3
3 4
4 5
3 5
4
-1 -2 -3 -4

View File

@ -120,6 +120,23 @@ struct pair_hash {
}
};
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 {
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) {
res1 = (res1 + x * pw1) % __array_hash_mdl1;
res2 = (res2 + x * 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 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];)