Submission #753058

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
753058	2023-06-04T14:03:24 Z	I_love_Hoang_Yen	Sequence (APIO23_sequence)	C++17	60 / 100	1405 ms	61372 KB

sequence

#include "sequence.h"
#include <bits/stdc++.h>
#define SZ(s) ((int) ((s).size()))
using namespace std;
 
bool is_sub_3(const std::vector<int> a) {
    auto mit = max_element(a.begin(), a.end());
    return std::is_sorted(a.begin(), mit)
        && std::is_sorted(mit, a.end(), std::greater<int>());
}
 
int len(const std::pair<int,int>& p) {
    return p.second - p.first + 1;
}
bool can_be_median(int cnt_less, int cnt_equal, int cnt_greater) {
    return cnt_equal + cnt_less >= cnt_greater;
}
 
int sub3(const vector<int>& a) {
    int n = SZ(a);
    unordered_map<int, vector<pair<int,int>>> pos;
    int l = 0;
    while (l < n) {
        int r = l;
        while (r < n && a[l] == a[r]) ++r;
        pos[a[l]].emplace_back(l, r-1);
        l = r;
    }
    int res = 0;
    for (const auto& [val, lrs] : pos) {
        // only 1 segment
        for (const auto& lr : lrs) res = max(res, len(lr));
 
        // 2 segments
        if (SZ(lrs) < 2) continue;
        assert(SZ(lrs) == 2);
        int cnt_equal = len(lrs[0]) + len(lrs[1]);
        int cnt_greater = len({lrs[0].second + 1, lrs[1].first - 1});
        int cnt_less = len({0, lrs[0].first - 1}) + len({lrs[1].second + 1, n-1});
        if (can_be_median(cnt_less, cnt_equal, cnt_greater)) {
            res = max(res, cnt_equal);
        }
    }
    return res;
}
 
// SegTree, copied from AtCoder library {{{
// AtCoder doc: https://atcoder.github.io/ac-library/master/document_en/segtree.html
//
// Notes:
// - Index of elements from 0 -> n-1
// - Range queries are [l, r-1]
//
// Tested:
// - (binary search) https://atcoder.jp/contests/practice2/tasks/practice2_j
// - https://oj.vnoi.info/problem/gss
// - https://oj.vnoi.info/problem/nklineup
// - (max_right & min_left for delete position queries) https://oj.vnoi.info/problem/segtree_itstr
// - https://judge.yosupo.jp/problem/point_add_range_sum
// - https://judge.yosupo.jp/problem/point_set_range_composite
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}
 
template<
    class T,  // data type for nodes
    T (*op) (T, T),  // operator to combine 2 nodes
    T (*e)() // identity element
>
struct SegTree {
    SegTree() : SegTree(0) {}
    explicit SegTree(int n) : SegTree(vector<T> (n, e())) {}
    explicit SegTree(const vector<T>& v) : _n((int) v.size()) {
        log = ceil_pow2(_n);
        size = 1<<log;
        d = vector<T> (2*size, e());
 
        for (int i = 0; i < _n; i++) d[size+i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }
 
    // 0 <= p < n
    void set(int p, T x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }
 
    // 0 <= p < n
    T get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }
 
    // Get product in range [l, r-1]
    // 0 <= l <= r <= n
    // For empty segment (l == r) -> return e()
    T prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        T sml = e(), smr = e();
        l += size;
        r += size;
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }
 
    T all_prod() const {
        return d[1];
    }
 
    // Binary search on SegTree to find largest r:
    //    f(op(a[l] .. a[r-1])) = true   (assuming empty array is always true)
    //    f(op(a[l] .. a[r])) = false    (assuming op(..., a[n]), which is out of bound, is always false)
    template <bool (*f)(T)> int max_right(int l) const {
        return max_right(l, [](T x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        T sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }
 
    // Binary search on SegTree to find smallest l:
    //    f(op(a[l] .. a[r-1])) = true      (assuming empty array is always true)
    //    f(op(a[l-1] .. a[r-1])) = false   (assuming op(a[-1], ..), which is out of bound, is always false)
    template <bool (*f)(T)> int min_left(int r) const {
        return min_left(r, [](T x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        T sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
 
private:
    int _n, size, log;
    vector<T> d;
 
    void update(int k) {
        d[k] = op(d[2*k], d[2*k+1]);
    }
};
// }}}
// SegTree examples {{{
// Examples: Commonly used SegTree ops: max / min / sum
struct MaxSegTreeOp {
    static int op(int x, int y) {
        return max(x, y);
    }
    static int e() {
        return INT_MIN;
    }
};
 
struct MinSegTreeOp {
    static int op(int x, int y) {
        return min(x, y);
    }
    static int e() {
        return INT_MAX;
    }
};
 
struct SumSegTreeOp {
    static long long op(long long x, long long y) {
        return x + y;
    }
    static long long e() {
        return 0;
    }
};
 
// using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>;
// using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>;
// using STSum = SegTree<int, SumSegTreeOp::op, SumSegTreeOp::e>;
// }}}
// Lazy Segment Tree, copied from AtCoder {{{
// Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html
//
// Notes:
// - Index of elements from 0
// - Range queries are [l, r-1]
// - composition(f, g) should return f(g())
//
// Tested:
// - https://oj.vnoi.info/problem/qmax2
// - https://oj.vnoi.info/problem/lites
// - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix
// - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder
// - https://atcoder.jp/contests/practice2/tasks/practice2_l
// - https://judge.yosupo.jp/problem/range_affine_range_sum

template<
    class S,                 // node data type
    S (*op) (S, S),          // combine 2 nodes
    S (*e) (),               // identity element
    class F,                 // lazy propagation tag
    S (*mapping) (F, S),     // apply tag F on a node
    F (*composition) (F, F), // combine 2 tags
    F (*id)()                // identity tag
>
struct LazySegTree {
    LazySegTree() : LazySegTree(0) {}
    explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {}
    explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) {
        log = ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    // 0 <= p < n
    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // 0 <= p < n
    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    // Get product in range [l, r-1]
    // 0 <= l <= r <= n
    // For empty segment (l == r) -> return e()
    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() {
        return d[1];
    }

    // 0 <= p < n
    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // Apply f on all elements in range [l, r-1]
    // 0 <= l <= r <= n
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    // Binary search on SegTree to find largest r:
    //    f(op(a[l] .. a[r-1])) = true   (assuming empty array is always true)
    //    f(op(a[l] .. a[r])) = false    (assuming op(..., a[n]), which is out of bound, is always false)
    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    // Binary search on SegTree to find smallest l:
    //    f(op(a[l] .. a[r-1])) = true      (assuming empty array is always true)
    //    f(op(a[l-1] .. a[r-1])) = false   (assuming op(a[-1], ..), which is out of bound, is always false)
    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }


private:
    int _n, size, log;
    vector<S> d;
    vector<F> lz;

    void update(int k) {
        d[k] = op(d[2*k], d[2*k+1]);
    }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2*k, lz[k]);
        all_apply(2*k+1, lz[k]);
        lz[k] = id();
    }
};
// }}}
 
int sub4(int n, const std::vector<int>& a) {
    int res = 0;
    int ln = *max_element(a.begin(), a.end());
    for (int median = 0; median <= ln; ++median) {
        vector<int> cnt_less(n, 0);
        vector<int> cnt_equal(n, 0);
        vector<int> cnt_greater(n, 0);
        for (int i = 0; i < n; ++i) {
            cnt_less[i] = a[i] < median;
            cnt_equal[i] = a[i] == median;
            cnt_greater[i] = a[i] > median;
        }
        std::partial_sum(cnt_less.begin(), cnt_less.end(), cnt_less.begin());
        std::partial_sum(cnt_equal.begin(), cnt_equal.end(), cnt_equal.begin());
        std::partial_sum(cnt_greater.begin(), cnt_greater.end(), cnt_greater.begin());
 
        //    cnt_less[r]   + cnt_equal[r]   - cnt_greater[r]
        // >= cnt_less[l-1] + cnt_equal[l-1] - cnt_greater[l-1]
        //
        //    cnt_less[r]   - cnt_equal[r]   - cnt_greater[r]
        //  < cnt_less[l-1] - cnt_equal[l-1] - cnt_greater[l-1]
        //
        //  l < r
        vector<vector<pair<int,int>>> f1_at(n*2 + 1);
        for (int i = n-1; i >= 0; --i) {
            // add n so that everything >= 0
            int f1 = cnt_less[i] + cnt_equal[i] - cnt_greater[i] + n;
            int f2 = cnt_less[i] - cnt_equal[i] - cnt_greater[i] + n;
            f1_at[f1].emplace_back(i, f2);
        }
        f1_at[n].emplace_back(-1, n);
 
        SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e> st(2*n + 1);
        for (int f1 = 2*n; f1 >= 0; --f1) {
            // f1(r) >= f1(l-1) && f2(r) < f2(l-1)
            for (const auto& [i, f2] : f1_at[f1]) {
                // l = i + 1
                int max_r = st.prod(0, f2 + 1);
                if (max_r > i) {
                    res = max(res, cnt_equal[max_r] - (i >= 0 ? cnt_equal[i] : 0));
                }
                // r = i
                st.set(f2, max(st.get(f2), i));
            }
        }
    }
    return res;
}

using F = int;
int mapping(F f, int s) {
    return f + s;
}
F composition(F f, F g) {
    return f + g;
}
F id() { return 0; }

bool can(int n, int eq, const vector<int>& a, const vector<vector<int>>& ids) {
    int ln = *max_element(a.begin(), a.end());
    LazySegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e, F, mapping, composition, id> st_max(n + 1);
    LazySegTree<int, MinSegTreeOp::op, MinSegTreeOp::e, F, mapping, composition, id> st_min(n + 1);
    st_max.set(0, 0);
    st_min.set(0, 0);
 
    for (int median = 0; median <= ln; median++) {
        if (median == 0) {
            for (int i = 1; i <= n; ++i) {
                st_max.set(i, i);
                st_min.set(i, i);
            }
        } else {
            // greater is affected?
            for (int i : ids[median]) {
                // previously: greater = 1, now: greater = 0
                st_max.apply(i, n+1, -1);
                st_min.apply(i, n+1, -1);
            }
            // less is affected?
            for (int i : ids[median-1]) {
                // previously: less = 0, now: less = 1
                st_max.apply(i, n+1, -1);
                st_min.apply(i, n+1, -1);
            }
        }
 
        if (SZ(ids[median]) < eq) continue;
        for (int ix = 0, iy = eq-1; iy < SZ(ids[median]); ++ix, ++iy) {
            int x = ids[median][ix];
            int y = ids[median][iy];
 
            // find [l, r]:
            // - l <= x < y <= r
            // - less + eq >= greater
            // - greater + eq >= less
            // - eq >= greater - less >= -eq
            // - eq >= (greater(r) - less(r)) - (greater(l-1) - less(l-1)) >= -eq
 
            int max_val = st_max.prod(y, n+1) - st_min.prod(0, x);
            int min_val = st_min.prod(y, n+1) - st_max.prod(0, x);
 
            // [-eq, eq] and [min_val, max_val] intersects
            if (min_val <= eq && max_val >= -eq) return true;
        }
    }
    return false;
}

int sub5(int n, std::vector<int> a) {
    // ids from 1
    a.insert(a.begin(), 0);
 
    vector<vector<int>> ids(n + 1);
    for (int i = 1; i <= n; ++i) {
        ids[a[i]].push_back(i);
    }
 
    int max_freq = 0;
    for (int i = 1; i <= n; ++i) {
        max_freq = max(max_freq, SZ(ids[i]));
    }
    int left = 1, right = max_freq, res = 1;
    while (left <= right) {
        int mid = (left + right) / 2;
        if (can(n, mid, a, ids)) {
            res = mid;
            left = mid + 1;
        } else {
            right = mid - 1;
        }
    }
    return res;
}
 
int sequence(int n, std::vector<int> a) {
    if (is_sub_3(a)) return sub3(a);
    if (n <= 2000 || *max_element(a.begin(), a.end()) <= 3) return sub4(n, a);
    return sub5(n, a);
}

Subtask #1

11.0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	2 ms	212 KB	Output is correct
5	Correct	1 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Correct	2 ms	212 KB	Output is correct
10	Correct	2 ms	212 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	2 ms	212 KB	Output is correct

Subtask #2

17.0 / 17.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	2 ms	212 KB	Output is correct
5	Correct	1 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Correct	2 ms	212 KB	Output is correct
10	Correct	2 ms	212 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	2 ms	212 KB	Output is correct
13	Correct	504 ms	516 KB	Output is correct
14	Correct	488 ms	552 KB	Output is correct
15	Correct	12 ms	468 KB	Output is correct
16	Correct	11 ms	468 KB	Output is correct
17	Correct	3 ms	468 KB	Output is correct
18	Correct	1 ms	468 KB	Output is correct
19	Correct	509 ms	548 KB	Output is correct
20	Correct	500 ms	544 KB	Output is correct
21	Correct	497 ms	520 KB	Output is correct
22	Correct	547 ms	528 KB	Output is correct

Subtask #3

7.0 / 7.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	155 ms	31664 KB	Output is correct
3	Correct	183 ms	31812 KB	Output is correct
4	Correct	34 ms	6096 KB	Output is correct
5	Correct	167 ms	29088 KB	Output is correct
6	Correct	167 ms	29104 KB	Output is correct
7	Correct	37 ms	6100 KB	Output is correct
8	Correct	39 ms	6096 KB	Output is correct
9	Correct	33 ms	6088 KB	Output is correct

Subtask #4

12.0 / 12.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	419 ms	61288 KB	Output is correct
3	Correct	432 ms	61344 KB	Output is correct
4	Correct	411 ms	61344 KB	Output is correct
5	Correct	426 ms	61372 KB	Output is correct
6	Correct	354 ms	61352 KB	Output is correct

Subtask #5

13.0 / 13.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1127 ms	47904 KB	Output is correct
2	Correct	1073 ms	47864 KB	Output is correct
3	Correct	483 ms	47340 KB	Output is correct
4	Correct	437 ms	47268 KB	Output is correct
5	Correct	756 ms	44208 KB	Output is correct
6	Correct	1190 ms	43936 KB	Output is correct
7	Correct	1142 ms	42756 KB	Output is correct
8	Correct	836 ms	42408 KB	Output is correct

Subtask #6

0.0 / 22.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	2 ms	212 KB	Output is correct
5	Correct	1 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Correct	2 ms	212 KB	Output is correct
10	Correct	2 ms	212 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	2 ms	212 KB	Output is correct
13	Correct	504 ms	516 KB	Output is correct
14	Correct	488 ms	552 KB	Output is correct
15	Correct	12 ms	468 KB	Output is correct
16	Correct	11 ms	468 KB	Output is correct
17	Correct	3 ms	468 KB	Output is correct
18	Correct	1 ms	468 KB	Output is correct
19	Correct	509 ms	548 KB	Output is correct
20	Correct	500 ms	544 KB	Output is correct
21	Correct	497 ms	520 KB	Output is correct
22	Correct	547 ms	528 KB	Output is correct
23	Correct	416 ms	8112 KB	Output is correct
24	Correct	297 ms	8200 KB	Output is correct
25	Correct	404 ms	8124 KB	Output is correct
26	Correct	888 ms	7192 KB	Output is correct
27	Correct	804 ms	7192 KB	Output is correct
28	Correct	971 ms	7192 KB	Output is correct
29	Correct	1313 ms	6936 KB	Output is correct
30	Correct	1279 ms	6976 KB	Output is correct
31	Correct	8 ms	1236 KB	Output is correct
32	Correct	20 ms	7784 KB	Output is correct
33	Correct	768 ms	8000 KB	Output is correct
34	Incorrect	1405 ms	8040 KB	Output isn't correct
35	Halted	0 ms	0 KB	-

Subtask #7

0.0 / 18.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	2 ms	212 KB	Output is correct
5	Correct	1 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	1 ms	212 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Correct	2 ms	212 KB	Output is correct
10	Correct	2 ms	212 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	2 ms	212 KB	Output is correct
13	Correct	504 ms	516 KB	Output is correct
14	Correct	488 ms	552 KB	Output is correct
15	Correct	12 ms	468 KB	Output is correct
16	Correct	11 ms	468 KB	Output is correct
17	Correct	3 ms	468 KB	Output is correct
18	Correct	1 ms	468 KB	Output is correct
19	Correct	509 ms	548 KB	Output is correct
20	Correct	500 ms	544 KB	Output is correct
21	Correct	497 ms	520 KB	Output is correct
22	Correct	547 ms	528 KB	Output is correct
23	Correct	155 ms	31664 KB	Output is correct
24	Correct	183 ms	31812 KB	Output is correct
25	Correct	34 ms	6096 KB	Output is correct
26	Correct	167 ms	29088 KB	Output is correct
27	Correct	167 ms	29104 KB	Output is correct
28	Correct	37 ms	6100 KB	Output is correct
29	Correct	39 ms	6096 KB	Output is correct
30	Correct	33 ms	6088 KB	Output is correct
31	Correct	419 ms	61288 KB	Output is correct
32	Correct	432 ms	61344 KB	Output is correct
33	Correct	411 ms	61344 KB	Output is correct
34	Correct	426 ms	61372 KB	Output is correct
35	Correct	354 ms	61352 KB	Output is correct
36	Correct	1127 ms	47904 KB	Output is correct
37	Correct	1073 ms	47864 KB	Output is correct
38	Correct	483 ms	47340 KB	Output is correct
39	Correct	437 ms	47268 KB	Output is correct
40	Correct	756 ms	44208 KB	Output is correct
41	Correct	1190 ms	43936 KB	Output is correct
42	Correct	1142 ms	42756 KB	Output is correct
43	Correct	836 ms	42408 KB	Output is correct
44	Correct	416 ms	8112 KB	Output is correct
45	Correct	297 ms	8200 KB	Output is correct
46	Correct	404 ms	8124 KB	Output is correct
47	Correct	888 ms	7192 KB	Output is correct
48	Correct	804 ms	7192 KB	Output is correct
49	Correct	971 ms	7192 KB	Output is correct
50	Correct	1313 ms	6936 KB	Output is correct
51	Correct	1279 ms	6976 KB	Output is correct
52	Correct	8 ms	1236 KB	Output is correct
53	Correct	20 ms	7784 KB	Output is correct
54	Correct	768 ms	8000 KB	Output is correct
55	Incorrect	1405 ms	8040 KB	Output isn't correct
56	Halted	0 ms	0 KB	-