#include <bits/stdc++.h>

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;
using u128 = unsigned __int128;

constexpr int inf = 1E9;
template<class Info>
struct SegmentTree {
    int n;
    std::vector<Info> info;
    SegmentTree() : n(0) {}
    SegmentTree(int n_, Info v_ = Info()) {
        init(n_, v_);
    }
    template<class T>
    SegmentTree(std::vector<T> init_) {
        init(init_);
    }
    void init(int n_, Info v_ = Info()) {
        init(std::vector(n_, v_));
    }
    template<class T>
    void init(std::vector<T> init_) {
        n = init_.size();
        info.assign(4 << std::__lg(n), Info());
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                info[p] = init_[l];
                return;
            }
            int m = (l + r) / 2;
            build(2 * p, l, m);
            build(2 * p + 1, m, r);
            pull(p);
        };
        build(1, 0, n);
    }
    void pull(int p) {
        info[p] = info[2 * p] + info[2 * p + 1];
    }
    void modify(int p, int l, int r, int x, const Info &v) {
        if (r - l == 1) {
            info[p] = v;
            return;
        }
        int m = (l + r) / 2;
        if (x < m) {
            modify(2 * p, l, m, x, v);
        } else {
            modify(2 * p + 1, m, r, x, v);
        }
        pull(p);
    }
    void modify(int p, const Info &v) {
        modify(1, 0, n, p, v);
    }
    Info rangeQuery(int p, int l, int r, int x, int y) {
        if (l >= y || r <= x) {
            return Info();
        }
        if (l >= x && r <= y) {
            return info[p];
        }
        int m = (l + r) / 2;
        return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
    }
    Info rangeQuery(int l, int r) {
        return rangeQuery(1, 0, n, l, r);
    }
    template<class F>
    int findFirst(int p, int l, int r, int x, int y, F &&pred) {
        if (l >= y || r <= x) {
            return -1;
        }
        if (l >= x && r <= y && !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findFirst(2 * p, l, m, x, y, pred);
        if (res == -1) {
            res = findFirst(2 * p + 1, m, r, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int l, int r, F &&pred) {
        return findFirst(1, 0, n, l, r, pred);
    }
    template<class F>
    int findLast(int p, int l, int r, int x, int y, F &&pred) {
        if (l >= y || r <= x) {
            return -1;
        }
        if (l >= x && r <= y && !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findLast(2 * p + 1, m, r, x, y, pred);
        if (res == -1) {
            res = findLast(2 * p, l, m, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int l, int r, F &&pred) {
        return findLast(1, 0, n, l, r, pred);
    }
};

struct Info {
    std::array<int, 2> a[21] {};
    int s = 0;
    int ans = 0;
    
    void add(int x, int c) {
        while (s > 1 && x > a[s - 1][0] && a[s - 2][0] > a[s - 1][0]) {
            auto [y, d] = a[--s];
            if (a[s - 1][0] == inf && x == inf) {
                continue;
            }
            if (d % 2 == 1) {
                if (d > 1) {
                    add(y + 1, d / 2);
                }
                add(inf, 1);
                if (d > 1) {
                    add(y + 1, d / 2);
                }
            } else {
                add(y + 1, d / 2);
            }
        }
        if (!s || a[s - 1][0] != x) {
            a[s++] = {x, c};
        } else {
            a[s - 1][1] += c;
        }
        if (a[s - 1][0] != inf) {
            ans = std::max(ans, a[s - 1][0] + std::__lg(a[s - 1][1]));
        }
    }
    
    Info() {}
    Info(int x) {
        a[s++] = {x, 1};
        ans = x == inf ? 0 : x;
    }
};

Info operator+(Info a, const Info &b) {
    a.ans = std::max(a.ans, b.ans);
    
    for (int i = 0; i < b.s; i++) {
        a.add(b.a[i][0], b.a[i][1]);
    }
    return a;
}

SegmentTree<Info> seg;
void prepare_game(std::vector<int> A) {
    int N = A.size();
    std::vector<Info> init(N);
    for (int i = 0; i < N; i++) {
        init[i] = A[i];
    }
    seg.init(init);
}

int play_game(int l, int r) {
    return (Info(inf) + seg.rangeQuery(l, r + 1) + Info(inf)).ans;
}

void update_game(int p, int v) {
    seg.modify(p, v);
}