답안 #1040897

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1040897	2024-08-01T11:33:32 Z	crimson231	경계 (BOI14_demarcation)	C++17	100 / 100	28 ms	9684 KB

demarcation

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <algorithm>
#include <vector>
#include <cassert>
#include <cmath>
#include <cstring>

/*
* 
* Splay tree / sweeping by jay0202
* Geometry by crimson231
* 
*/

//#define JAY_MODULE_DEBUG
//#define CRIMSON_MODULE_DEBUG

typedef long long ll;
typedef double ld;
typedef std::vector<int> Vint;
const int LEN = 1e5 + 1;

int N;
ll memo[LEN];
std::vector<int> g[LEN]; // above lines
struct Pos {
    int x, y;
    Pos(int X = 0, int Y = 0) : x(X), y(Y) {}
    bool operator == (const Pos& p) const { return x == p.x && y == p.y; }
    bool operator != (const Pos& p) const { return x != p.x || y != p.y; }
    bool operator < (const Pos& p) const { return x == p.x ? y < p.y : x < p.x; }
    Pos operator + (const Pos& p) const { return { x + p.x, y + p.y }; }
    Pos operator - (const Pos& p) const { return { x - p.x, y - p.y }; }
    Pos operator * (const int& n) const { return { x * n, y * n }; }
    Pos operator / (const int& n) const { return { x / n, y / n }; }
    ll operator * (const Pos& p) const { return (ll)x * p.x + (ll)y * p.y; }
    ll operator / (const Pos& p) const { return (ll)x * p.y - (ll)y * p.x; }
    Pos& operator += (const Pos& p) { x += p.x; y += p.y; return *this; }
    Pos& operator *= (const int& scale) { x *= scale; y *= scale; return *this; }
    Pos operator - () const { return { -x, -y }; }
    Pos operator ~ () const { return { -y, x }; }
    friend std::istream& operator >> (std::istream& is, Pos& p) { is >> p.x >> p.y; return is; }
    friend std::ostream& operator << (std::ostream& os, const Pos& p) { os << p.x << " " << p.y; return os; }
} pos[LEN];
const Pos O = Pos(0, 0);
typedef std::vector<Pos> Polygon;
ll cross(const Pos& d1, const Pos& d2, const Pos& d3) { return (d2 - d1) / (d3 - d2); }
int ccw(const Pos& d1, const Pos& d2, const Pos& d3) { ll ret = cross(d1, d2, d3); return ret < 0 ? -1 : !!ret; }
ll area(Pos H[], const int& sz) {
    ll ret = 0;
    for (int i = 0; i < sz; i++) ret += H[i] / H[(i + 1) % sz];
    return ret;
}
ll area(std::vector<Pos>& H) {
    ll ret = 0;
    int sz = H.size();
    for (int i = 0; i < sz; i++) ret += H[i] / H[(i + 1) % sz];
    return ret;
}
void norm(Pos H[], const int& sz) {
    ll A = area(H, sz); assert(A);
    if (A < 0) std::reverse(H, H + sz);
}
void norm(Polygon& H) {
    ll A = area(H); assert(A);
    if (A < 0) std::reverse(H.begin(), H.end());
    auto s = std::min_element(H.begin(), H.end());
    std::rotate(H.begin(), s, H.end());
}
void move(Polygon& H, const Pos& vec) {
    int sz = H.size();
    for (int i = 0; i < sz; i++) H[i] += vec;
}
void rotate() { for (int i = 0; i < N; i++) pos[i] = ~pos[i]; }
void rotate(Polygon& H) {
    int sz = H.size();
    for (int i = 0; i < sz; i++) H[i] = ~H[i];
}
void mirror(Polygon& H) {
    int sz = H.size();
    for (int i = 0; i < sz; i++) H[i].x = -H[i].x;
}
inline bool polygon_cmp(const Polygon& A, const Polygon& B) {
    int a = A.size(), b = B.size();
    if (a != b) return 0;
    for (int i = 0; i < a; i++) if (A[i] != B[i]) return 0;
    return 1;
}
bool operator == (const Polygon& p, const Polygon& q) { return polygon_cmp(p, q); }
Polygon cut_polygon(int u, int v, Pos s, Pos e) {
    Polygon H, tmp;
    Vint V;
    //std::cout << "make poly:: " << u << " " << v << "\n";
    //std::cout << "s, e:: " << s << " " << e << "\n";
    H.push_back(e);
    H.push_back(s);
    for (int i = (u + 1) % N; i != (v + 1) % N; i = (i + 1) % N) {
        const Pos& p = pos[i];
        if (p != s && p != e) H.push_back(p);
    }
    int sz = H.size();
    V.resize(sz, 0);
    for (int i = 0; i < sz; i++) {
        const Pos& pre = H[(i - 1 + sz) % sz], & cur = H[i], & nxt = H[(i + 1) % sz];
        if (!ccw(pre, cur, nxt)) V[i] = 1;
    }
    for (int i = 0; i < sz; i++) if (!V[i]) tmp.push_back(H[i]);
    return tmp;
}
bool all_polygon_cmp(int u, int v, Pos s, Pos e) {
    Polygon A = cut_polygon(u, v, s, e);
    Polygon B = cut_polygon(v, u, e, s);
#ifdef CRIMSON_MODULE_DEBUG
    std::cout << "FUCK:: s:: " << s << " e:: " << e << "\n";
    std::cout << "A = [\n";
    for (Pos& p : A) {
        std::cout << "(" << p.x << ", " << p.y << "), \n";
    }
    std::cout << "]\n";
    std::cout << "B = [\n";
    for (Pos& p : B) {
        std::cout << "(" << p.x << ", " << p.y << "), \n";
    }
    std::cout << "]\n";
#endif
    if (A.size() != B.size()) return 0;
    norm(B);
    const Pos& b = B[0];
    for (int i = 0; i < 2; i++) {
        for (int j = 0; j < 4; j++) {
            rotate(A);
            norm(A);
            const Pos& a = A[0];
            move(A, b - a);
            if (A == B) return 1;
        }
        mirror(A);
    }
    return 0;
}
struct Line {
    int y;      // y coord
    int l, r;   // x coords (l <= r)

    /// <summary>
    /// sort lines
    /// <para>
    /// 1. compare y.
    /// </para>
    /// <para>
    /// 2. if y coords are equal, compare x.
    /// </para>
    /// </summary>
    /// <param name="o">other</param>
    /// <returns>bool</returns>
    bool operator<(const Line& o) const {
        return y == o.y ? l < o.l : y > o.y;
    }
};
int Q;
/// <summary>
/// event horizon
/// </summary>
struct Event {
    int i; // index of event line
    int d; // flag value. (0: insert range, 1: query range)
    Line l; // line
    bool operator<(const Event& r) const { return l < r.l; }
} events[LEN];
/// <summary>
/// segment struct defined to use in SplayTree node.
/// simplified version of line event (ommited y coord)
/// </summary>
struct Seg {
    int l, r; // x coords
    int i;
    Seg(int l = 0, int r = 0, int i = 0) : l(l), r(r), i(i) {}
    /// <summary>
    /// only compare x coords
    /// </summary>
    /// <param name="o">other</param>
    /// <returns></returns>
    bool operator<(const Seg& o) const {
        return l < o.l;
    }
};
std::vector<Seg> segs;
void match(int u, int v, int l, int r) {
#ifdef JAY_MODULE_DEBUG
    std::cout << "facing pair: " << u << ' ' << v << '\n';
    std::cout << "    facing range: " << l << ' ' << r << '\n';
    g[u].push_back(v);
#endif
    segs.push_back(Seg(l, r, v));
}
/// <summary>
/// find a segment that divides the area of hole polygon in half.
/// </summary>
/// <param name="i">query's idx</param>
/// <param name="S">target segment</param>
/// <param name="s">split seg's end point 1</param>
/// <param name="e">split seg's end point 2</param>
/// <returns>boolean, if true, compose split segment { s - e }.</returns>
bool find_split(const int i, const Seg& S, Pos& s, Pos& e) {
    int j = i, k = S.i;
    const Pos& J = pos[j], & K = pos[k];
    bool f = 0;
    if (k < j) f = 1, std::swap(j, k);
    ll a1 = memo[k] - memo[j];
    //std::cout << "FUCK:: a1:: " << a1 << "\n";
    //std::cout << "FUCK:: A :: " << memo[N] << "\n";
    if (f) a1 = memo[N] - a1;
    Pos& pl = pos[i], & pr = pos[(i + 1) % N];
    assert(pl.x < pr.x);
    int r = std::min(pr.x, S.r);
    int l = std::max(pl.x, S.l);
    int yh = pos[S.i].y;
    int yl = pl.y;
    int h = yh - yl;
    Pos b1 = Pos(r, yh), b2 = Pos(l, yh), b3 = Pos(l, yl), b4 = Pos(r, yl);
    /*
         sl b2 b1 sr == K <--...
    J == pl b3 b4 pr ------->... a1
    */
    ll amax = a1 + K / b2 + b2 / b3 + b3 / J;
    ll amin = a1 + K / b1 + b1 / b4 + b4 / J;
    ll a2 = memo[N] >> 1;
    //std::cout << "DEBUG:: amin:: " << amin << " amax:: " << amax << " a2:: " << a2 << "\n";
    if (amin <= a2 && a2 <= amax) {
        ll box = a2 - amin;
        ll w = box / h;
        if (w & 1) return 0;
        s = Pos(r - (w >> 1), pr.y);
        e = Pos(r - (w >> 1), pos[S.i].y);
        assert(s < e);
        return 1;
    }
    return 0;
}
class SplayTree {
    struct Node {
        Node* l;
        Node* r;
        Node* p;
        Seg val;
        Node(int l, int r, int i) : l(0), r(0), p(0) { val = { l, r, i }; }
        ~Node() { if (l) delete l; if (r) delete r; }
    } *root;
    void rotate(Node* x) {
        Node* p = x->p;
        if (!p) return;
        Node* b = 0;
        if (x == p->l) {
            p->l = b = x->r;
            x->r = p;
        }
        else {
            p->r = b = x->l;
            x->l = p;
        }
        x->p = p->p;
        p->p = x;
        if (b) b->p = p;
        (x->p ? p == x->p->l ? x->p->l : x->p->r : root) = x;
    }
    void splay(Node* x) {
        while (x->p) {
            Node* p = x->p;
            Node* g = p->p;
            if (g) {
                if ((x == p->l) == (p == g->l)) rotate(p);
                else rotate(x);
            }
            rotate(x);
        }
    }

    /// <summary>
    /// find a line that has nearest r coord from l.  
    /// </summary>
    /// <param name="l">: target x coord</param>
    /// <returns></returns>
    Node* find(int l) {
        if (!root) return 0;

        Node* p = root;
        while (1) {
            if (p->val.r == l) break;
            if (p->val.r < l) {
                if (!p->r) {
                    break;
                }
                p = p->r;
            }
            else {
                if (!p->l) {
                    break;
                }
                p = p->l;
            }
        }
        splay(p);
        return p;
    }

public:
    SplayTree() : root(0) {}
    ~SplayTree() { if (root) delete root; }
    void insert(int l, int r, int i) {
        if (!root) {
            root = new Node(l, r, i);
            return;
        }
        Node* p = root;
        Node** pp;
        while (1) {
            if (p->val.l < l) {
                if (!p->r) {
                    pp = &p->r;
                    break;
                }
                p = p->r;
            }
            else {
                if (!p->l) {
                    pp = &p->l;
                    break;
                }
                p = p->l;
            }
        }
        Node* x = new Node(l, r, i);
        *pp = x;
        x->p = p;
        splay(x);
    }
    void pop(Node* ptr) {
        if (!ptr) return;
        splay(ptr);
        Node* p = root;
        if (p->l && p->r) {
            root = p->l; root->p = 0;
            Node* l = root;
            while (l->r) l = l->r;
            l->r = p->r;
            p->r->p = l;
        }
        else if (p->l) root = p->l, root->p = 0;
        else if (p->r) root = p->r, root->p = 0;
        else root = 0;
        p->l = p->r = 0;
        delete p;
    }

    /// <summary>
    /// find leftmost line first.
    /// if line is splitted by query segment, then insert new segment and return.
    /// else, find right segments while r coord of segment is smaller than query r.
    /// </summary>
    /// <param name="l">x coord</param>
    /// <param name="r">x coord</param>
    /// <param name="i">line index</param>
    void query(int l, int r, int i) {
        assert(root);

        Node* x = find(l); // first segment
        assert(x->val.l <= l);

        if (x->val.r < l) { // if segment is out of range: find very right one
            x = x->r;
            while (x->l) x = x->l;
        }

        if (x->val.r > r) { // if splitted
            match(i, x->val.i, l, r);
            int nl = r, nr = x->val.r, ni = x->val.i;
            x->val.r = l; // split
            if (x->val.l == l) pop(x); // and pop if left is covered.
            insert(nl, nr, ni); // insert new right segment
            return;
        }

        match(i, x->val.i, l, x->val.r); // match two of them
        x->val.r = l; // left side of segment is covered by query segment
        if (x->val.r == x->val.l) pop(x); // pop if all range covered

        while (x = find(l)) { // find leftmost
            //if (x->val.r == l) break;
            if (x->val.r <= l) { // if leftmost is out of range
                if (!x->r) return; // no more right segment
                x = x->r;
                while (x->l) x = x->l; // find very right segment
            }
            if (x->val.l > r) return;
            match(i, x->val.i, x->val.l, std::min(r, x->val.r)); // match two of them
            if (x->val.r > r) { // if right segment is not covered totally
                x->val.l = r;
                break; // then, query range is sweeped. return
            }
            else pop(x); // else, a segment is sweeped. pop and find next segment
        }
    }
} sp;
bool vertical_split(Pos& s, Pos& e) {
    memo[0] = 0;
    for (int i = 0; i < N; i++) {
        memo[i + 1] = memo[i] + pos[i] / pos[(i + 1) % N];
    }
    // horizontal check
    Q = 0;
    for (int i = 0; i < N; ++i) {
        int j = (i + 1) % N;
        if (pos[i].y == pos[j].y) {
            if (pos[i].x < pos[j].x) { // right halfline
                events[Q++] = { i, 1, { pos[i].y, pos[i].x, pos[j].x } };
            }
            if (pos[i].x > pos[j].x) { // left halfline
                events[Q++] = { i, 0, { pos[i].y, pos[j].x, pos[i].x } };
            }
        }
    }

    std::sort(events, events + Q);

    for (int i = 0; i < Q; ++i) {
        //std::cout << (events[i].d == 0 ? "insert" : "query") << " segment: (h, l, r) ";
        //std::cout << events[i].l.y << ' ' << events[i].l.l << ' ' << events[i].l.r << '\n';
        if (events[i].d == 0) sp.insert(events[i].l.l, events[i].l.r, events[i].i);
        if (events[i].d == 1) {
            segs.clear();
            sp.query(events[i].l.l, events[i].l.r, events[i].i);
            for (Seg& S : segs) {
                //std::cout << "segs::\n";
                if (find_split(events[i].i, S, s, e)) {
                    //std::cout << "polygon cmp before::\n";
                    if (all_polygon_cmp(events[i].i, S.i, s, e)) return 1;
                    //std::cout << "polygon cmp after::\n";
                }
            }
        }
    }

#ifdef JAY_MODULE_DEBUG
    for (int i = 0; i <= N; ++i) {
        if (g[i].size()) {
            std::cout << "right half-line from " << i << '\n';
            std::cout << "    matching left half-lines from: ";
            for (const int& j : g[i]) std::cout << j << ' ';
            std::cout << '\n';
        }
    }
#endif
    return 0;
}
void solve() {
    //freopen("demarcation.in copy.14", "r", stdin);
    //freopen("demarcation.out", "w", stdout);
    std::cin.tie(0)->sync_with_stdio(0);
    //std::cout.tie(0);
    std::cin >> N;
    for (int i = 0; i < N; ++i) std::cin >> pos[i].x >> pos[i].y;
    ll A = area(pos, N);
    assert(A);
    if (A < 0) std::reverse(pos, pos + N);
    A *= -1;
    A >>= 1;
#ifdef CRIMSON_MODULE_DEBUG
    std::cout << "pos = [\n";
    for (int i = 0; i < N; i++) {
        std::cout << "(" << pos[i].x << ", " << pos[i].y << "), \n";
    }
    std::cout << "]\n";
#endif
    if (A & 1) { std::cout << "NO\n"; return; }

    Pos s, e;
    if (vertical_split(s, e)) {
        for (int i = 0; i < N; i++) {
            if (pos[i].x == e.x && s.y < pos[i].y && e.y > pos[i].y)
                e = pos[i];
        }
        std::cout << s << " " << e << "\n";
        return;
    }
    rotate();
    if (vertical_split(s, e)) {
        for (int i = 0; i < N; i++) {
            if (pos[i].x == e.x && s.y < pos[i].y && e.y > pos[i].y)
                e = pos[i];
        }
        std::cout << -~s << " " << -~e << "\n";
        return;
    }
    std::cout << "NO\n";
    return;
}
int main() { solve(); return 0; }//boj10098 Demarcation

Compilation message

demarcation.cpp: In member function 'void SplayTree::query(int, int, int)':
demarcation.cpp:388:18: warning: suggest parentheses around assignment used as truth value [-Wparentheses]
  388 |         while (x = find(l)) { // find leftmost
      |                ~~^~~~~~~~~

Subtask #1

12.0 / 12.0

#	결과	실행 시간	메모리	Grader output
1	Correct	3 ms	5724 KB	Output is correct
2	Correct	1 ms	5292 KB	Output is correct
3	Correct	1 ms	5348 KB	Output is correct
4	Correct	3 ms	5724 KB	Output is correct
5	Correct	1 ms	5212 KB	Output is correct
6	Correct	1 ms	5212 KB	Output is correct
7	Correct	1 ms	5208 KB	Output is correct
8	Correct	1 ms	5212 KB	Output is correct
9	Correct	18 ms	8536 KB	Output is correct
10	Correct	1 ms	5212 KB	Output is correct
11	Correct	2 ms	5212 KB	Output is correct
12	Correct	1 ms	5212 KB	Output is correct
13	Correct	1 ms	5344 KB	Output is correct

Subtask #2

15.0 / 15.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	5212 KB	Output is correct
2	Correct	1 ms	5348 KB	Output is correct
3	Correct	1 ms	5212 KB	Output is correct
4	Correct	1 ms	5212 KB	Output is correct
5	Correct	1 ms	5212 KB	Output is correct
6	Correct	1 ms	5212 KB	Output is correct
7	Correct	1 ms	5292 KB	Output is correct
8	Correct	1 ms	5212 KB	Output is correct
9	Correct	1 ms	5212 KB	Output is correct
10	Correct	1 ms	5208 KB	Output is correct
11	Correct	1 ms	5212 KB	Output is correct
12	Correct	1 ms	5212 KB	Output is correct
13	Correct	1 ms	5212 KB	Output is correct
14	Correct	1 ms	5212 KB	Output is correct
15	Correct	1 ms	5212 KB	Output is correct
16	Correct	1 ms	5212 KB	Output is correct
17	Correct	1 ms	5212 KB	Output is correct
18	Correct	1 ms	5212 KB	Output is correct
19	Correct	1 ms	5212 KB	Output is correct
20	Correct	1 ms	5212 KB	Output is correct
21	Correct	1 ms	5212 KB	Output is correct
22	Correct	1 ms	5208 KB	Output is correct
23	Correct	1 ms	5212 KB	Output is correct
24	Correct	1 ms	5212 KB	Output is correct
25	Correct	1 ms	5212 KB	Output is correct
26	Correct	1 ms	5212 KB	Output is correct
27	Correct	1 ms	5212 KB	Output is correct
28	Correct	1 ms	5212 KB	Output is correct
29	Correct	1 ms	5212 KB	Output is correct
30	Correct	1 ms	5212 KB	Output is correct

Subtask #3

23.0 / 23.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	5212 KB	Output is correct
2	Correct	1 ms	5212 KB	Output is correct
3	Correct	2 ms	5212 KB	Output is correct
4	Correct	1 ms	5212 KB	Output is correct
5	Correct	1 ms	5212 KB	Output is correct
6	Correct	1 ms	5212 KB	Output is correct
7	Correct	1 ms	5212 KB	Output is correct
8	Correct	1 ms	5212 KB	Output is correct
9	Correct	1 ms	5208 KB	Output is correct
10	Correct	1 ms	5344 KB	Output is correct
11	Correct	1 ms	5212 KB	Output is correct
12	Correct	1 ms	5212 KB	Output is correct
13	Correct	1 ms	5212 KB	Output is correct
14	Correct	1 ms	5212 KB	Output is correct
15	Correct	1 ms	5212 KB	Output is correct
16	Correct	1 ms	5212 KB	Output is correct
17	Correct	1 ms	5212 KB	Output is correct
18	Correct	1 ms	5212 KB	Output is correct
19	Correct	1 ms	5212 KB	Output is correct
20	Correct	1 ms	5212 KB	Output is correct
21	Correct	1 ms	5212 KB	Output is correct
22	Correct	2 ms	5208 KB	Output is correct
23	Correct	1 ms	5212 KB	Output is correct
24	Correct	1 ms	5212 KB	Output is correct
25	Correct	1 ms	5212 KB	Output is correct
26	Correct	1 ms	5212 KB	Output is correct
27	Correct	1 ms	5212 KB	Output is correct
28	Correct	1 ms	5212 KB	Output is correct
29	Correct	1 ms	5376 KB	Output is correct
30	Correct	1 ms	5212 KB	Output is correct
31	Correct	1 ms	5212 KB	Output is correct
32	Correct	1 ms	5468 KB	Output is correct
33	Correct	1 ms	5292 KB	Output is correct
34	Correct	1 ms	5212 KB	Output is correct
35	Correct	1 ms	5212 KB	Output is correct
36	Correct	2 ms	5212 KB	Output is correct
37	Correct	1 ms	5212 KB	Output is correct
38	Correct	2 ms	5468 KB	Output is correct
39	Correct	1 ms	5212 KB	Output is correct

Subtask #4

50.0 / 50.0

#	결과	실행 시간	메모리	Grader output
1	Correct	3 ms	5724 KB	Output is correct
2	Correct	1 ms	5212 KB	Output is correct
3	Correct	2 ms	5212 KB	Output is correct
4	Correct	3 ms	5724 KB	Output is correct
5	Correct	1 ms	5212 KB	Output is correct
6	Correct	1 ms	5212 KB	Output is correct
7	Correct	1 ms	5212 KB	Output is correct
8	Correct	1 ms	5208 KB	Output is correct
9	Correct	18 ms	8448 KB	Output is correct
10	Correct	1 ms	5212 KB	Output is correct
11	Correct	1 ms	5212 KB	Output is correct
12	Correct	1 ms	5212 KB	Output is correct
13	Correct	1 ms	5208 KB	Output is correct
14	Correct	1 ms	5212 KB	Output is correct
15	Correct	1 ms	5212 KB	Output is correct
16	Correct	1 ms	5212 KB	Output is correct
17	Correct	1 ms	5212 KB	Output is correct
18	Correct	1 ms	5212 KB	Output is correct
19	Correct	1 ms	5208 KB	Output is correct
20	Correct	1 ms	5212 KB	Output is correct
21	Correct	1 ms	5212 KB	Output is correct
22	Correct	1 ms	5212 KB	Output is correct
23	Correct	1 ms	5212 KB	Output is correct
24	Correct	1 ms	5212 KB	Output is correct
25	Correct	1 ms	5212 KB	Output is correct
26	Correct	1 ms	5212 KB	Output is correct
27	Correct	1 ms	5212 KB	Output is correct
28	Correct	1 ms	5212 KB	Output is correct
29	Correct	1 ms	5208 KB	Output is correct
30	Correct	1 ms	5212 KB	Output is correct
31	Correct	1 ms	5212 KB	Output is correct
32	Correct	1 ms	5208 KB	Output is correct
33	Correct	1 ms	5212 KB	Output is correct
34	Correct	1 ms	5212 KB	Output is correct
35	Correct	1 ms	5468 KB	Output is correct
36	Correct	1 ms	5212 KB	Output is correct
37	Correct	1 ms	5212 KB	Output is correct
38	Correct	2 ms	5464 KB	Output is correct
39	Correct	2 ms	5212 KB	Output is correct
40	Correct	1 ms	5212 KB	Output is correct
41	Correct	1 ms	5468 KB	Output is correct
42	Correct	1 ms	5300 KB	Output is correct
43	Correct	1 ms	5468 KB	Output is correct
44	Correct	13 ms	6960 KB	Output is correct
45	Correct	11 ms	7040 KB	Output is correct
46	Correct	7 ms	6552 KB	Output is correct
47	Correct	5 ms	5724 KB	Output is correct
48	Correct	5 ms	6236 KB	Output is correct
49	Correct	18 ms	8108 KB	Output is correct
50	Correct	13 ms	7936 KB	Output is correct
51	Correct	20 ms	8064 KB	Output is correct
52	Correct	24 ms	9404 KB	Output is correct
53	Correct	9 ms	5212 KB	Output is correct
54	Correct	21 ms	8032 KB	Output is correct
55	Correct	9 ms	6580 KB	Output is correct
56	Correct	18 ms	8320 KB	Output is correct
57	Correct	28 ms	6236 KB	Output is correct
58	Correct	22 ms	9560 KB	Output is correct
59	Correct	24 ms	9684 KB	Output is correct
60	Correct	8 ms	5724 KB	Output is correct
61	Correct	4 ms	5724 KB	Output is correct
62	Correct	6 ms	6236 KB	Output is correct
63	Correct	8 ms	6592 KB	Output is correct
64	Correct	9 ms	6492 KB	Output is correct
65	Correct	6 ms	5376 KB	Output is correct
66	Correct	17 ms	8536 KB	Output is correct