Submission #1099844

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1099844	2024-10-12T05:35:24 Z	model_code	Hieroglyphs (IOI24_hieroglyphs)	C++17	100 / 100	423 ms	20216 KB

hieroglyphs

// correct/author-full.cpp

#include "hieroglyphs.h"
#include<bits/stdc++.h>

using namespace std;

using vi = vector<int>;
using vvi = vector<vi>;

//erases non-common elements
void clean(vi& a, vi& b) {
    vi ap;
    vi bp;
    set<int> as;
    set<int> bs;
    for (int x : a) as.insert(x);
    for (int x : b) bs.insert(x);
    for (int x : a) if (bs.count(x)) ap.push_back(x);
    for (int x : b) if (as.count(x)) bp.push_back(x);
    swap(a, ap);
    swap(b, bp);
}

map<int, int> coordinate_compress(vi& a, vi& b) {
    int cc = 0;
    map<int, int> mp;
    map<int, int> rmp;
    for (int& x : a) {
        if (!mp.count(x)) {
            mp[x] = cc++;
            rmp[mp[x]] = x;
        }
        x = mp[x];
    }
    for (int& x : b) {
        if (!mp.count(x)) {
            mp[x] = cc++;
            rmp[mp[x]] = x;
        }
        x = mp[x];
    }
    return rmp;
}

bool is_subsequence(const vi& a, const vi& b) {
    int j = 0;
    for (int x : a) {
        if (j < (int)b.size() && b[j] == x) {
            j++;
        }
    }
    return j == (int)b.size();
}

vector<int> get_candidate(vector<int> a, vector<int> b) {
    int n = a.size();
    int m = b.size();

    vi occ_a(max(n, m)+1, 0);
    vi occ_b(max(n, m)+1, 0);
    for (int i=0; i < n; ++i) {
        occ_a[a[i]]++;
    }
    for (int i=0; i < m; ++i) {
        occ_b[b[i]]++;
    }

    vi c;
    queue<int> qa;
    queue<int> qb;

    for (int i=0; i < n; ++i) {
        if (occ_a[a[i]] <= occ_b[a[i]]) {
            qa.push(i);
        }
    }
    for (int i=0; i < m; ++i) {
        if (occ_a[b[i]] > occ_b[b[i]]) {
            qb.push(i);
        }
    }

    int i_a_curr = 0;
    int i_b_curr = 0;
    int i_a_next = 0;
    int i_b_next = 0;
    vi occ_a_curr = vi(occ_a);
    vi occ_a_next = vi(occ_a);
    vi occ_b_curr = vi(occ_b);
    vi occ_b_next = vi(occ_b);

    while(!qa.empty() && !qb.empty()) {
        while(i_a_next < qa.front()) {
            occ_a_next[a[i_a_next]]--;
            i_a_next++;
        }
        while(i_b_next < qb.front()) {
            occ_b_next[b[i_b_next]]--;
            i_b_next++;
        }

        int x = a[i_a_next];
        int y = b[i_b_next];

        int occ_x = occ_a_next[x];
        int occ_y = occ_b_next[y];

        bool a_good = (occ_a_next[y] >= occ_y && occ_b_curr[x] > occ_b_next[x]);
        bool b_good = (occ_b_next[x] >= occ_x && occ_a_curr[y] > occ_a_next[y]);

        if (a_good && b_good) return vi();
        if (!a_good && !b_good) return vi();

        if(a_good) {
            c.push_back(x);
            qa.pop();
            while(i_a_curr <= i_a_next) {
                occ_a_curr[a[i_a_curr]]--;
                i_a_curr++;
            }
            while(b[i_b_curr] != x) {
                occ_b_curr[b[i_b_curr]]--;
                i_b_curr++;
            }
            occ_b_curr[b[i_b_curr]]--;
            i_b_curr++;
        }
        else {
            c.push_back(y);
            qb.pop();
            while(i_b_curr <= i_b_next) {
                occ_b_curr[b[i_b_curr]]--;
                i_b_curr++;
            }
            while(a[i_a_curr] != y) {
                occ_a_curr[a[i_a_curr]]--;
                i_a_curr++;
            }
            occ_a_curr[a[i_a_curr]]--;
            i_a_curr++;
        }
    }

    while(!qa.empty()) {
        c.push_back(a[qa.front()]);
        qa.pop();
    }
    while(!qb.empty()) {
        c.push_back(b[qb.front()]);
        qb.pop();
    }

    return ((is_subsequence(a, c) && is_subsequence(b, c)) ? c : vi());
}




//returns v of size |b|
//v[i] = smallest index so that there exists a common subsequence of a[0..v[i]] and b[0..i] that is not
// a common subsequence of a[0..v[i]] and b[0..i-1]. if such index does not exist, v[i] = |a|
vector<int> index_vector(const vi& a, const vi& b) {
    int n = a.size();
    int m = b.size();
    vi v(m);
    int max_v = 0;
    for (int x : a) max_v = max(x, max_v);
    for (int x : b) max_v = max(x, max_v);
    vi prev_occ_b(max_v+1, -1);
    vvi a_occ(max_v+1);
    for (int i=0; i < n; ++i) {
        a_occ[a[i]].push_back(i);
    }
    for (int i=0; i <= max_v; ++i) {
        a_occ[i].push_back(n);
    }
    vector<pair<int, int>> min_stack;
    for (int i=0; i < m; ++i) {
        if (prev_occ_b[b[i]] == -1) {
            v[i] = a_occ[b[i]][0];
        }
        else {
            int min_val = lower_bound(min_stack.begin(), min_stack.end(), pair<int, int>(prev_occ_b[b[i]], -1))->second;
            if (min_val < n) v[i] = *lower_bound(a_occ[b[i]].begin(), a_occ[b[i]].end(), min_val+1);
            else v[i] = n;
        }
        while(!min_stack.empty() && min_stack.back().second >= v[i]) {
            min_stack.pop_back();
        }
        min_stack.emplace_back(i, v[i]);
        prev_occ_b[b[i]] = i;
    }
    return v; 
}

// RMQ template from KACTL
template<class T>
struct RMQ {
	vector<vector<T>> jmp;
	RMQ(const vector<T>& V) : jmp(1, V) {
		for (int pw = 1, k = 1; pw * 2 <= (int)V.size(); pw *= 2, ++k) {
			jmp.emplace_back((int)V.size() - pw * 2 + 1);
			for (int j=0; j < (int)jmp[k].size(); ++j)
				jmp[k][j] = min(jmp[k - 1][j], jmp[k - 1][j + pw]);
		}
	}
	T query(int a, int b) {
		int dep = 31 - __builtin_clz(b - a);
		return min(jmp[dep][a], jmp[dep][b - (1 << dep)]);
	}
};

bool no_single_crossing(const vi& a, const vi& b, const vi& c) {
    int n = a.size();
    int m = b.size();
    int l = c.size(); 

    vi rb = vi(b);
    reverse(rb.begin(), rb.end());

    vi rc = vi(c);
    reverse(rc.begin(), rc.end());

    vi v_ab = index_vector(a, b);
    vi v_rbc = index_vector(rb, rc);
    
    RMQ<int> v_rbc_rmq = RMQ<int>(v_rbc);

    vi v_max_rc_i(n+1);
    v_max_rc_i[n] = 0;
    for (int i=n-1; i >= 0; --i) {
        v_max_rc_i[i] = v_max_rc_i[i+1];
        if (a[i] == rc[v_max_rc_i[i+1]]) {
            v_max_rc_i[i]++;
        }
        if (v_max_rc_i[i] > l) v_max_rc_i[i] = l;
    }
    vi v_min_rc_i(m+1);
    v_min_rc_i[0] = l-1;
    for (int i=0; i < m; ++i) {
        v_min_rc_i[i+1] = v_min_rc_i[i];
        if (b[i] == rc[v_min_rc_i[i]]) {
            v_min_rc_i[i+1]--;
        }
        if (v_min_rc_i[i] < -1) v_min_rc_i[i] = -1;
    }

    for (int j=0; j < m; ++j) {
        int ai = v_ab[j];
        if (ai == n) continue;
        int min_rc_i = v_min_rc_i[j+1];
        int max_rc_i = v_max_rc_i[ai+1];
        if (min_rc_i+1 < max_rc_i && v_rbc_rmq.query(min_rc_i+1, max_rc_i) + j < m-1) return false;
    }
    return true;
}

bool verify(const vi& a, const vi& b, const vi& c) {
    if (c.empty()) return false;
    return no_single_crossing(a, b, c) && no_single_crossing(b, a, c);    
}

vector<int> ucs(vector<int> a, vector<int> b) {
    clean(a, b);
    if (a.empty() || b.empty()) {
		return vector<int>();
    }
    map<int, int> mp = coordinate_compress(a, b);
    vi c = get_candidate(a, b);
    if (verify(a, b, c)) {
        for (int& x : c) x = mp[x];

		return c;
    }
    return vector<int>({-1});
}

Subtask #0

0.0 / 0.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct

Subtask #1

3.0 / 3.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	3 ms	604 KB	Output is correct
4	Correct	1 ms	344 KB	Output is correct
5	Correct	367 ms	20216 KB	Output is correct
6	Correct	283 ms	15620 KB	Output is correct
7	Correct	278 ms	15572 KB	Output is correct

Subtask #2

15.0 / 15.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	3 ms	604 KB	Output is correct
4	Correct	1 ms	344 KB	Output is correct
5	Correct	367 ms	20216 KB	Output is correct
6	Correct	283 ms	15620 KB	Output is correct
7	Correct	278 ms	15572 KB	Output is correct
8	Correct	264 ms	13092 KB	Output is correct
9	Correct	248 ms	13196 KB	Output is correct
10	Correct	207 ms	12968 KB	Output is correct
11	Correct	202 ms	13212 KB	Output is correct
12	Correct	213 ms	13080 KB	Output is correct
13	Correct	208 ms	12960 KB	Output is correct
14	Correct	196 ms	13116 KB	Output is correct
15	Correct	214 ms	13132 KB	Output is correct
16	Correct	201 ms	13184 KB	Output is correct
17	Correct	256 ms	13104 KB	Output is correct
18	Correct	1 ms	348 KB	Output is correct
19	Correct	1 ms	348 KB	Output is correct
20	Correct	1 ms	348 KB	Output is correct
21	Correct	4 ms	604 KB	Output is correct
22	Correct	89 ms	7240 KB	Output is correct
23	Correct	195 ms	11928 KB	Output is correct
24	Correct	179 ms	11776 KB	Output is correct
25	Correct	171 ms	11828 KB	Output is correct
26	Correct	130 ms	6508 KB	Output is correct
27	Correct	290 ms	12996 KB	Output is correct
28	Correct	306 ms	12992 KB	Output is correct
29	Correct	222 ms	13004 KB	Output is correct
30	Correct	224 ms	12972 KB	Output is correct
31	Correct	218 ms	13040 KB	Output is correct
32	Correct	256 ms	12960 KB	Output is correct
33	Correct	215 ms	13012 KB	Output is correct
34	Correct	222 ms	11916 KB	Output is correct
35	Correct	194 ms	13080 KB	Output is correct
36	Correct	219 ms	13028 KB	Output is correct
37	Correct	202 ms	13124 KB	Output is correct
38	Correct	167 ms	13112 KB	Output is correct
39	Correct	174 ms	13096 KB	Output is correct
40	Correct	337 ms	13100 KB	Output is correct
41	Correct	205 ms	13076 KB	Output is correct
42	Correct	174 ms	13204 KB	Output is correct
43	Correct	334 ms	13104 KB	Output is correct
44	Correct	242 ms	13104 KB	Output is correct
45	Correct	165 ms	13076 KB	Output is correct
46	Correct	179 ms	13168 KB	Output is correct
47	Correct	173 ms	13180 KB	Output is correct
48	Correct	167 ms	13212 KB	Output is correct
49	Correct	193 ms	13084 KB	Output is correct
50	Correct	241 ms	13076 KB	Output is correct
51	Correct	242 ms	13140 KB	Output is correct
52	Correct	212 ms	13068 KB	Output is correct
53	Correct	386 ms	12972 KB	Output is correct
54	Correct	170 ms	13096 KB	Output is correct
55	Correct	192 ms	12984 KB	Output is correct
56	Correct	423 ms	13096 KB	Output is correct
57	Correct	169 ms	12996 KB	Output is correct
58	Correct	168 ms	13112 KB	Output is correct
59	Correct	168 ms	13052 KB	Output is correct
60	Correct	202 ms	13332 KB	Output is correct
61	Correct	207 ms	13064 KB	Output is correct
62	Correct	170 ms	13156 KB	Output is correct
63	Correct	159 ms	13100 KB	Output is correct
64	Correct	195 ms	13160 KB	Output is correct
65	Correct	199 ms	13076 KB	Output is correct
66	Correct	208 ms	13088 KB	Output is correct
67	Correct	249 ms	13188 KB	Output is correct
68	Correct	198 ms	13100 KB	Output is correct
69	Correct	0 ms	348 KB	Output is correct
70	Correct	1 ms	348 KB	Output is correct

Subtask #3

10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	69 ms	10828 KB	Output is correct
2	Correct	71 ms	11112 KB	Output is correct
3	Correct	52 ms	6972 KB	Output is correct
4	Correct	48 ms	6792 KB	Output is correct
5	Correct	63 ms	10048 KB	Output is correct
6	Correct	19 ms	4104 KB	Output is correct
7	Correct	1 ms	348 KB	Output is correct
8	Correct	0 ms	348 KB	Output is correct
9	Correct	1 ms	348 KB	Output is correct
10	Correct	1 ms	348 KB	Output is correct
11	Correct	0 ms	348 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	1 ms	344 KB	Output is correct
14	Correct	1 ms	348 KB	Output is correct
15	Correct	1 ms	344 KB	Output is correct
16	Correct	58 ms	9876 KB	Output is correct
17	Correct	33 ms	5552 KB	Output is correct
18	Correct	34 ms	5632 KB	Output is correct
19	Correct	14 ms	4872 KB	Output is correct
20	Correct	52 ms	7828 KB	Output is correct
21	Correct	18 ms	5044 KB	Output is correct
22	Correct	16 ms	5444 KB	Output is correct
23	Correct	31 ms	10932 KB	Output is correct
24	Correct	32 ms	10912 KB	Output is correct
25	Correct	16 ms	6468 KB	Output is correct
26	Correct	36 ms	10916 KB	Output is correct

Subtask #4

16.0 / 16.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	264 ms	13092 KB	Output is correct
2	Correct	248 ms	13196 KB	Output is correct
3	Correct	207 ms	12968 KB	Output is correct
4	Correct	202 ms	13212 KB	Output is correct
5	Correct	213 ms	13080 KB	Output is correct
6	Correct	208 ms	12960 KB	Output is correct
7	Correct	196 ms	13116 KB	Output is correct
8	Correct	214 ms	13132 KB	Output is correct
9	Correct	201 ms	13184 KB	Output is correct
10	Correct	256 ms	13104 KB	Output is correct
11	Correct	1 ms	348 KB	Output is correct
12	Correct	1 ms	348 KB	Output is correct
13	Correct	1 ms	348 KB	Output is correct
14	Correct	4 ms	604 KB	Output is correct
15	Correct	89 ms	7240 KB	Output is correct
16	Correct	195 ms	11928 KB	Output is correct
17	Correct	179 ms	11776 KB	Output is correct
18	Correct	171 ms	11828 KB	Output is correct
19	Correct	130 ms	6508 KB	Output is correct
20	Correct	69 ms	10828 KB	Output is correct
21	Correct	71 ms	11112 KB	Output is correct
22	Correct	52 ms	6972 KB	Output is correct
23	Correct	48 ms	6792 KB	Output is correct
24	Correct	63 ms	10048 KB	Output is correct
25	Correct	19 ms	4104 KB	Output is correct
26	Correct	1 ms	600 KB	Output is correct
27	Correct	1 ms	348 KB	Output is correct
28	Correct	2 ms	348 KB	Output is correct
29	Correct	1 ms	348 KB	Output is correct
30	Correct	1 ms	348 KB	Output is correct
31	Correct	2 ms	604 KB	Output is correct
32	Correct	2 ms	604 KB	Output is correct
33	Correct	2 ms	604 KB	Output is correct
34	Correct	12 ms	2412 KB	Output is correct
35	Correct	50 ms	10008 KB	Output is correct
36	Correct	71 ms	10984 KB	Output is correct
37	Correct	54 ms	11012 KB	Output is correct
38	Correct	65 ms	10804 KB	Output is correct
39	Correct	60 ms	11072 KB	Output is correct
40	Correct	177 ms	12168 KB	Output is correct
41	Correct	104 ms	9284 KB	Output is correct
42	Correct	27 ms	4932 KB	Output is correct
43	Correct	31 ms	5036 KB	Output is correct
44	Correct	28 ms	5044 KB	Output is correct
45	Correct	34 ms	4668 KB	Output is correct
46	Correct	165 ms	9460 KB	Output is correct
47	Correct	220 ms	9528 KB	Output is correct
48	Correct	154 ms	9440 KB	Output is correct
49	Correct	184 ms	8868 KB	Output is correct
50	Correct	167 ms	8868 KB	Output is correct
51	Correct	137 ms	8872 KB	Output is correct
52	Correct	183 ms	8392 KB	Output is correct
53	Correct	166 ms	8368 KB	Output is correct
54	Correct	144 ms	8404 KB	Output is correct
55	Correct	17 ms	2500 KB	Output is correct
56	Correct	88 ms	10984 KB	Output is correct
57	Correct	69 ms	9856 KB	Output is correct
58	Correct	85 ms	11560 KB	Output is correct
59	Correct	117 ms	10976 KB	Output is correct
60	Correct	190 ms	10340 KB	Output is correct

Subtask #5

14.0 / 14.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	1 ms	348 KB	Output is correct
4	Correct	1 ms	348 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	1 ms	344 KB	Output is correct
8	Correct	1 ms	348 KB	Output is correct
9	Correct	1 ms	344 KB	Output is correct
10	Correct	1 ms	600 KB	Output is correct
11	Correct	1 ms	348 KB	Output is correct
12	Correct	2 ms	348 KB	Output is correct
13	Correct	1 ms	348 KB	Output is correct
14	Correct	1 ms	348 KB	Output is correct
15	Correct	2 ms	604 KB	Output is correct
16	Correct	2 ms	604 KB	Output is correct
17	Correct	2 ms	604 KB	Output is correct
18	Correct	5 ms	604 KB	Output is correct
19	Correct	5 ms	604 KB	Output is correct
20	Correct	4 ms	604 KB	Output is correct
21	Correct	6 ms	716 KB	Output is correct
22	Correct	4 ms	604 KB	Output is correct
23	Correct	4 ms	604 KB	Output is correct
24	Correct	4 ms	604 KB	Output is correct
25	Correct	5 ms	668 KB	Output is correct
26	Correct	3 ms	604 KB	Output is correct
27	Correct	2 ms	604 KB	Output is correct
28	Correct	5 ms	720 KB	Output is correct
29	Correct	3 ms	604 KB	Output is correct
30	Correct	2 ms	728 KB	Output is correct
31	Correct	2 ms	604 KB	Output is correct
32	Correct	2 ms	604 KB	Output is correct
33	Correct	0 ms	348 KB	Output is correct
34	Correct	1 ms	348 KB	Output is correct
35	Correct	1 ms	348 KB	Output is correct
36	Correct	1 ms	348 KB	Output is correct
37	Correct	2 ms	348 KB	Output is correct
38	Correct	2 ms	344 KB	Output is correct
39	Correct	2 ms	348 KB	Output is correct
40	Correct	0 ms	348 KB	Output is correct
41	Correct	1 ms	348 KB	Output is correct
42	Correct	2 ms	604 KB	Output is correct
43	Correct	1 ms	604 KB	Output is correct
44	Correct	1 ms	604 KB	Output is correct

Subtask #6

42.0 / 42.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct
6	Correct	3 ms	604 KB	Output is correct
7	Correct	1 ms	344 KB	Output is correct
8	Correct	367 ms	20216 KB	Output is correct
9	Correct	283 ms	15620 KB	Output is correct
10	Correct	278 ms	15572 KB	Output is correct
11	Correct	264 ms	13092 KB	Output is correct
12	Correct	248 ms	13196 KB	Output is correct
13	Correct	207 ms	12968 KB	Output is correct
14	Correct	202 ms	13212 KB	Output is correct
15	Correct	213 ms	13080 KB	Output is correct
16	Correct	208 ms	12960 KB	Output is correct
17	Correct	196 ms	13116 KB	Output is correct
18	Correct	214 ms	13132 KB	Output is correct
19	Correct	201 ms	13184 KB	Output is correct
20	Correct	256 ms	13104 KB	Output is correct
21	Correct	1 ms	348 KB	Output is correct
22	Correct	1 ms	348 KB	Output is correct
23	Correct	1 ms	348 KB	Output is correct
24	Correct	4 ms	604 KB	Output is correct
25	Correct	89 ms	7240 KB	Output is correct
26	Correct	195 ms	11928 KB	Output is correct
27	Correct	179 ms	11776 KB	Output is correct
28	Correct	171 ms	11828 KB	Output is correct
29	Correct	130 ms	6508 KB	Output is correct
30	Correct	290 ms	12996 KB	Output is correct
31	Correct	306 ms	12992 KB	Output is correct
32	Correct	222 ms	13004 KB	Output is correct
33	Correct	224 ms	12972 KB	Output is correct
34	Correct	218 ms	13040 KB	Output is correct
35	Correct	256 ms	12960 KB	Output is correct
36	Correct	215 ms	13012 KB	Output is correct
37	Correct	222 ms	11916 KB	Output is correct
38	Correct	194 ms	13080 KB	Output is correct
39	Correct	219 ms	13028 KB	Output is correct
40	Correct	202 ms	13124 KB	Output is correct
41	Correct	167 ms	13112 KB	Output is correct
42	Correct	174 ms	13096 KB	Output is correct
43	Correct	337 ms	13100 KB	Output is correct
44	Correct	205 ms	13076 KB	Output is correct
45	Correct	174 ms	13204 KB	Output is correct
46	Correct	334 ms	13104 KB	Output is correct
47	Correct	242 ms	13104 KB	Output is correct
48	Correct	165 ms	13076 KB	Output is correct
49	Correct	179 ms	13168 KB	Output is correct
50	Correct	173 ms	13180 KB	Output is correct
51	Correct	167 ms	13212 KB	Output is correct
52	Correct	193 ms	13084 KB	Output is correct
53	Correct	241 ms	13076 KB	Output is correct
54	Correct	242 ms	13140 KB	Output is correct
55	Correct	212 ms	13068 KB	Output is correct
56	Correct	386 ms	12972 KB	Output is correct
57	Correct	170 ms	13096 KB	Output is correct
58	Correct	192 ms	12984 KB	Output is correct
59	Correct	423 ms	13096 KB	Output is correct
60	Correct	169 ms	12996 KB	Output is correct
61	Correct	168 ms	13112 KB	Output is correct
62	Correct	168 ms	13052 KB	Output is correct
63	Correct	202 ms	13332 KB	Output is correct
64	Correct	207 ms	13064 KB	Output is correct
65	Correct	170 ms	13156 KB	Output is correct
66	Correct	159 ms	13100 KB	Output is correct
67	Correct	195 ms	13160 KB	Output is correct
68	Correct	199 ms	13076 KB	Output is correct
69	Correct	208 ms	13088 KB	Output is correct
70	Correct	249 ms	13188 KB	Output is correct
71	Correct	198 ms	13100 KB	Output is correct
72	Correct	0 ms	348 KB	Output is correct
73	Correct	1 ms	348 KB	Output is correct
74	Correct	69 ms	10828 KB	Output is correct
75	Correct	71 ms	11112 KB	Output is correct
76	Correct	52 ms	6972 KB	Output is correct
77	Correct	48 ms	6792 KB	Output is correct
78	Correct	63 ms	10048 KB	Output is correct
79	Correct	19 ms	4104 KB	Output is correct
80	Correct	1 ms	348 KB	Output is correct
81	Correct	0 ms	348 KB	Output is correct
82	Correct	1 ms	348 KB	Output is correct
83	Correct	1 ms	348 KB	Output is correct
84	Correct	0 ms	348 KB	Output is correct
85	Correct	0 ms	348 KB	Output is correct
86	Correct	1 ms	344 KB	Output is correct
87	Correct	1 ms	348 KB	Output is correct
88	Correct	1 ms	344 KB	Output is correct
89	Correct	58 ms	9876 KB	Output is correct
90	Correct	33 ms	5552 KB	Output is correct
91	Correct	34 ms	5632 KB	Output is correct
92	Correct	14 ms	4872 KB	Output is correct
93	Correct	52 ms	7828 KB	Output is correct
94	Correct	18 ms	5044 KB	Output is correct
95	Correct	16 ms	5444 KB	Output is correct
96	Correct	31 ms	10932 KB	Output is correct
97	Correct	32 ms	10912 KB	Output is correct
98	Correct	16 ms	6468 KB	Output is correct
99	Correct	36 ms	10916 KB	Output is correct
100	Correct	1 ms	600 KB	Output is correct
101	Correct	1 ms	348 KB	Output is correct
102	Correct	2 ms	348 KB	Output is correct
103	Correct	1 ms	348 KB	Output is correct
104	Correct	1 ms	348 KB	Output is correct
105	Correct	2 ms	604 KB	Output is correct
106	Correct	2 ms	604 KB	Output is correct
107	Correct	2 ms	604 KB	Output is correct
108	Correct	12 ms	2412 KB	Output is correct
109	Correct	50 ms	10008 KB	Output is correct
110	Correct	71 ms	10984 KB	Output is correct
111	Correct	54 ms	11012 KB	Output is correct
112	Correct	65 ms	10804 KB	Output is correct
113	Correct	60 ms	11072 KB	Output is correct
114	Correct	177 ms	12168 KB	Output is correct
115	Correct	104 ms	9284 KB	Output is correct
116	Correct	27 ms	4932 KB	Output is correct
117	Correct	31 ms	5036 KB	Output is correct
118	Correct	28 ms	5044 KB	Output is correct
119	Correct	34 ms	4668 KB	Output is correct
120	Correct	165 ms	9460 KB	Output is correct
121	Correct	220 ms	9528 KB	Output is correct
122	Correct	154 ms	9440 KB	Output is correct
123	Correct	184 ms	8868 KB	Output is correct
124	Correct	167 ms	8868 KB	Output is correct
125	Correct	137 ms	8872 KB	Output is correct
126	Correct	183 ms	8392 KB	Output is correct
127	Correct	166 ms	8368 KB	Output is correct
128	Correct	144 ms	8404 KB	Output is correct
129	Correct	17 ms	2500 KB	Output is correct
130	Correct	88 ms	10984 KB	Output is correct
131	Correct	69 ms	9856 KB	Output is correct
132	Correct	85 ms	11560 KB	Output is correct
133	Correct	117 ms	10976 KB	Output is correct
134	Correct	190 ms	10340 KB	Output is correct
135	Correct	5 ms	604 KB	Output is correct
136	Correct	5 ms	604 KB	Output is correct
137	Correct	4 ms	604 KB	Output is correct
138	Correct	6 ms	716 KB	Output is correct
139	Correct	4 ms	604 KB	Output is correct
140	Correct	4 ms	604 KB	Output is correct
141	Correct	4 ms	604 KB	Output is correct
142	Correct	5 ms	668 KB	Output is correct
143	Correct	3 ms	604 KB	Output is correct
144	Correct	2 ms	604 KB	Output is correct
145	Correct	5 ms	720 KB	Output is correct
146	Correct	3 ms	604 KB	Output is correct
147	Correct	2 ms	728 KB	Output is correct
148	Correct	2 ms	604 KB	Output is correct
149	Correct	2 ms	604 KB	Output is correct
150	Correct	0 ms	348 KB	Output is correct
151	Correct	1 ms	348 KB	Output is correct
152	Correct	1 ms	348 KB	Output is correct
153	Correct	1 ms	348 KB	Output is correct
154	Correct	2 ms	348 KB	Output is correct
155	Correct	2 ms	344 KB	Output is correct
156	Correct	2 ms	348 KB	Output is correct
157	Correct	0 ms	348 KB	Output is correct
158	Correct	1 ms	348 KB	Output is correct
159	Correct	2 ms	604 KB	Output is correct
160	Correct	1 ms	604 KB	Output is correct
161	Correct	1 ms	604 KB	Output is correct
162	Correct	109 ms	9960 KB	Output is correct
163	Correct	8 ms	1116 KB	Output is correct
164	Correct	15 ms	1744 KB	Output is correct
165	Correct	32 ms	3284 KB	Output is correct
166	Correct	61 ms	5116 KB	Output is correct
167	Correct	99 ms	8092 KB	Output is correct
168	Correct	18 ms	4932 KB	Output is correct
169	Correct	27 ms	4960 KB	Output is correct
170	Correct	30 ms	4928 KB	Output is correct
171	Correct	24 ms	4660 KB	Output is correct
172	Correct	10 ms	1360 KB	Output is correct
173	Correct	10 ms	1300 KB	Output is correct
174	Correct	12 ms	1520 KB	Output is correct
175	Correct	9 ms	1256 KB	Output is correct
176	Correct	10 ms	1496 KB	Output is correct
177	Correct	13 ms	1616 KB	Output is correct
178	Correct	114 ms	10240 KB	Output is correct
179	Correct	124 ms	10196 KB	Output is correct
180	Correct	127 ms	9412 KB	Output is correct
181	Correct	112 ms	9512 KB	Output is correct
182	Correct	114 ms	9312 KB	Output is correct
183	Correct	118 ms	9408 KB	Output is correct
184	Correct	122 ms	8612 KB	Output is correct
185	Correct	131 ms	8764 KB	Output is correct
186	Correct	121 ms	8800 KB	Output is correct
187	Correct	107 ms	8748 KB	Output is correct
188	Correct	115 ms	8240 KB	Output is correct
189	Correct	135 ms	8336 KB	Output is correct
190	Correct	111 ms	8268 KB	Output is correct
191	Correct	104 ms	8396 KB	Output is correct
192	Correct	133 ms	9372 KB	Output is correct
193	Correct	167 ms	9520 KB	Output is correct
194	Correct	123 ms	9508 KB	Output is correct
195	Correct	121 ms	9416 KB	Output is correct
196	Correct	158 ms	8768 KB	Output is correct
197	Correct	116 ms	8892 KB	Output is correct
198	Correct	121 ms	8868 KB	Output is correct
199	Correct	108 ms	8876 KB	Output is correct
200	Correct	113 ms	8412 KB	Output is correct
201	Correct	109 ms	8272 KB	Output is correct
202	Correct	106 ms	8360 KB	Output is correct
203	Correct	95 ms	8368 KB	Output is correct
204	Correct	179 ms	9552 KB	Output is correct
205	Correct	127 ms	9332 KB	Output is correct
206	Correct	151 ms	9428 KB	Output is correct
207	Correct	113 ms	9432 KB	Output is correct
208	Correct	119 ms	8628 KB	Output is correct
209	Correct	115 ms	8816 KB	Output is correct
210	Correct	106 ms	8872 KB	Output is correct
211	Correct	104 ms	8864 KB	Output is correct
212	Correct	127 ms	8204 KB	Output is correct
213	Correct	111 ms	8332 KB	Output is correct
214	Correct	99 ms	8332 KB	Output is correct
215	Correct	95 ms	8232 KB	Output is correct
216	Correct	16 ms	2380 KB	Output is correct
217	Correct	40 ms	11068 KB	Output is correct
218	Correct	38 ms	9744 KB	Output is correct
219	Correct	72 ms	11676 KB	Output is correct
220	Correct	76 ms	10992 KB	Output is correct
221	Correct	104 ms	10216 KB	Output is correct