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) {
        if (b[p].val == INF) return;
        pushtag(p * 2, left_len, b[p]);
        pushtag(p * 2 + 1, right_len, b[p]);
        b[p] = tag_type();
    }
    void pushtag(size_type p, size_type len, const tag_type& c) {
        if (d[p].mx <= c.val) return;
        d[p].val += (c.val - d[p].mx) * d[p].cnt;
        d[p].mx = c.val;
        b[p] = c;
    }
    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);
        pull(p);
    }

    void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) {
        if (d[p].mx <= c.val) return;
        if (l <= s && t <= r && d[p].se < c.val) {
            pushtag(p, t - s + 1, 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 = INF;
};
struct Info {
    ll val = 0, mx = 0, se = 0, cnt = 0;
};
Info operator+(const Info &a, const Info &b) {
    if (a.mx == b.mx) {
        return {
            .val = a.val + b.val,
            .mx = a.mx,
            .se = max(a.se, b.se),
            .cnt = a.cnt + b.cnt,
        };
    } else if (a.mx > b.mx) {
        return {
            .val = a.val + b.val,
            .mx = a.mx,
            .se = max(a.se, b.mx),
            .cnt = a.cnt,
        };
    } else {
        return {
            .val = a.val + b.val,
            .mx = b.mx,
            .se = max(a.mx, b.se),
            .cnt = b.cnt,
        };
    }
}


// Default leaves:
// Info {
//     .val = INFLL,
//     .mx = INFLL,
//     .se = 0,
//     .cnt = 1,
// }