oj.uz

Submission #914867

# Submission time Handle Problem Language Result Execution time Memory
914867 2024-01-22T19:26:12 Z bobbilyking Radio Towers (IOI22_towers) C++17
100 / 100
 812 ms 56000 KB 
/*

step 1. we really only care about peaks and valleys of the array
step 2. once we have the list of peaks, precompute the valleys to the left and right of each peak. The "glue value" of the peak is Height[peak] - max(Height[left valley], Height[right valley]), which the maximum D value allowed s.t. this peak can be the transmission tower between the two adjacent valleys

Step 3. Put these peaks in a 2d segtree, represetning (position, value, original index in array). This segtree needs to be able to support:

    // Queries in the range [l, r] for all res values (peaks with glue value) >= D, and then returns 
    // how many items were in the range, the minimum indexed peak, and maximum indexed peak of said range.

Step 4. The answer is simply doing the above query, this gets us the # of peaks, then do some fixing on the endpoints to make sure that the left and right endpoints are valid valleys or not.

Proof of why this works:

Intuitively, what the final construction is doing is using the peaks as "glue" values for the valleys and then verifying that all gaps work. 

The construction works as a lower bound, since by definition of how we put things into the segtree, the valleys on both sides are valid to select (except as an endpoint). Even if we skip peaks, if two peaks satisfy the >=D property, one of the valleys on both sides must satisfy it. 

(WLOG, Let's say H[peak_l] < H[peak_r], and both are selected. This means that H[right_valley[peak_l]] is a valid transition point).

So all glue points work, we can select a valley between any of them. We just need to take care about the valleys on the endpoints, but that is an easy fix. 

To show this is an upper bound: (SKETCH)

First recall that only peaks are useful as "glue" and valleys are useful as chosen towers (except at endpoints which we handle already).

With our segtree query, we only ever query peaks in the range with a sufficiently high glue value, so we need to show that having one of these peaks without a sufficiently high glue value will never work.

Well, that's easy: "insufficient glue value" means that we can't pick both of the adjacent valleys in our answer; we can only pick one of them. But if we can only pick one of them, then there's no point in using this peak as a glue value. So our query is correct in not picking this peak as a glue value.

What about the endpoints: Notice that the endpoints can only make not-valleys seem like valleys, i.e. shrink the effective D value, so we're only ever selecting a potentially incorrect glue value, and fixing it afterwards; we never miss a candidate solution. 

====================================================================================================================

	[ a bit confusing argument down below] 

	- Formally, you'd first make the claim that glue towers must be peaks; this can be shown fairly easily. Then, you use an exchange argument: The two valleys adjacent to a useless peak can't be selected, so we must select only one of them. Like this
	
	Originally, we have
	
	P V (useless peak) V P 
	
	First, (useless peak) cannot join the two V's by definition. So we can't select both V's. So we only select one of them. WLOG select the left V.
	
	P V | (useless peak) _ P
	
	If we selected P as glue in our query, that means height(P) > height(useless peak), since the useless valley contributed to both of their precomps.  
	
	If we didn't, you can probably propogate the value until we actually select a glue P and gg.

The "fixing" side is hard to express here but it should be clear in the code
*/

#include "towers.h"

#include <bits/stdc++.h>
using namespace std;
typedef int ll;
using pl = pair<ll, ll>;
using vl = vector<ll>;
#define F(i, l, r) for (ll i = ll(l); i < ll(r); ++i)
#define FD(i, l, r) for (ll i = ll(l); i > ll(r); --i)
#define A(a) (a).begin(), (a).end()
#define K first
#define V second

template<typename T> struct SparseTable {
    int n,log2=0;
    function<T(T, T)> merge;
    T id ;
    vector<vector<T>> a = {{}};
    SparseTable(const vector<T>& v, function<T(T, T)> _merge, T _id): merge(_merge), id(_id) {
        n = v.size();
        while((1<<log2) <= n) {
            ++log2;
        }
        a.resize(log2);
        a[0] = v;
        for(int i=1,len=1;i<log2;++i,len*=2) {
            a[i].resize(n + 1 - (1<<i));
            for(size_t j=0;j<a[i].size();++j) {
                a[i][j] = merge(a[i-1][j], a[i-1][j + len]);
            }
        }
    }
    SparseTable(){}
    T query(int l, int r) { // [l,r)
        if (r <= l) return id;
        int len = __lg(r-l);
        return merge(a[len][l], a[len][r- (1<<len)]);
    }   
};

SparseTable<ll> spmin;
 

const int MAXN = 100010, INF = 1000000010;

namespace seg {
    pl merge(pl a, pl b) {
        return pair(min(a.K, b.K), max(a.V, b.V));
    }

    struct node{    
        vector<pl> vec;
        vector<pl> indices; // {mn, mx}
        node(){};
        node(int value, int pos){
            vec.emplace_back(value, pos);
            indices.emplace_back(pos, pos);
        }
        node(node& a, node& b){
            vec.resize(a.vec.size() + b.vec.size());
            indices.resize(vec.size());
            merge(a.vec.begin(), a.vec.end(), b.vec.begin(), b.vec.end(), vec.begin());
            pl cur(MAXN, -1);

            // All items are now in sorted order, relative to first key.
            // mn and max represent the range of indices 
            FD(i, ll(vec.size())-1, -1) indices[i] = cur = merge(pair(vec[i].V, vec[i].V), cur);
        }
    };

    node tr[2*MAXN];

    pair<int, pl> query(int l, int r, int x){
        int cnt=0;
        pl res(MAXN, -1);

        auto handle = [&](node& cur) {
            auto &[vec, indices] = cur;
            auto itr = lower_bound(A(vec), pair(x, -1));
            int pos = (int)(itr - vec.begin());
            cnt += (int)(vec.end() - itr);
            if(itr!=vec.end()) res = merge(res, indices[pos]);
        };

        for(l+=MAXN, r+=MAXN; l<r; l>>=1, r>>=1){
            if(l&1) handle(tr[l++]);
            if(r&1) handle(tr[--r]);
        }

        return {cnt, res};
    }

    void build(vl res) {
        F(i, 0, res.size()) seg::tr[MAXN+i]=seg::node(res[i], i);
        FD(i, MAXN-1, -1) tr[i]=node(tr[i<<1], tr[i<<1|1]);
    }
}
 
 
int arr[MAXN];
 
void init(int n, vector<int> H) {
    vl maxl(n), maxr(n);
    copy(A(H), arr);

    spmin = SparseTable<ll>(H, [](ll a, ll b) {
        return min(a, b);
    }, INF);

    F(i, 0, n) {
        int x;
        for(x=i-1; x!=-1 && H[x]<H[i]; x=maxl[x]);
        maxl[i]=x;
    }

    FD(i, n-1, -1) {
        int x;
        for(x=i+1; x!=n && H[x]<H[i]; x=maxr[x]);
        maxr[i]=x;
    }
    // maxl and maxr finds closest node greater than it to left and right ? not sure 

    vl res(n);

    F(i, 0, n) {
        int l = maxl[i], r = maxr[i];
        // H[i] is trying to glue the left and right, so it must take the max of 
        // the two valleys to either side.
        res[i] = H[i] - max(spmin.query(l+1, i), spmin.query(i+1, r));
    }

    seg::build(res);
}
 
int max_towers(int L, int R, int D) {
    // Queries in the range [l, r] for all res values (peaks with glue value) >= D, and then returns 
    // how many items were in the range, the minimum indexed peak, and maximum indexed peak of said range.
    auto [cnt, indices] = seg::query(L, R+1, D);
    if(!cnt) return 1;
    auto [mn, mx] = indices;

    // we want to find something to lease to the left and right
    // since we're only counting peaks (we actually lease valleys)
    // we would like to lease (cnt+1) things since (cnt+1) gaps,
    // but need to make sure endpoints are legit

    bool sa = (D > arr[mn] - spmin.query(L, mn));
    bool sb = (D > arr[mx] - spmin.query(mx+1, R+1));

    return max(1, (cnt + 1) - sa - sb);
}

Subtask #1
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 308 ms 36952 KB Output is correct
2 Correct 688 ms 55752 KB Output is correct
3 Correct 678 ms 55760 KB Output is correct
4 Correct 625 ms 55760 KB Output is correct
5 Correct 646 ms 55888 KB Output is correct
6 Correct 641 ms 55888 KB Output is correct
7 Correct 610 ms 55756 KB Output is correct
8 Correct 3 ms 9816 KB Output is correct
9 Correct 4 ms 10840 KB Output is correct
10 Correct 4 ms 10824 KB Output is correct

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10072 KB Output is correct
2 Correct 5 ms 10840 KB Output is correct
3 Correct 5 ms 10840 KB Output is correct
4 Correct 4 ms 10840 KB Output is correct
5 Correct 5 ms 10840 KB Output is correct
6 Correct 5 ms 10840 KB Output is correct
7 Correct 4 ms 10840 KB Output is correct
8 Correct 5 ms 10840 KB Output is correct
9 Correct 4 ms 10840 KB Output is correct
10 Correct 4 ms 10840 KB Output is correct
11 Correct 4 ms 10840 KB Output is correct
12 Correct 3 ms 9904 KB Output is correct
13 Correct 6 ms 11096 KB Output is correct
14 Correct 4 ms 10872 KB Output is correct
15 Correct 6 ms 10840 KB Output is correct
16 Correct 5 ms 10820 KB Output is correct
17 Correct 4 ms 10840 KB Output is correct
18 Correct 6 ms 10816 KB Output is correct
19 Correct 5 ms 10840 KB Output is correct
20 Correct 4 ms 10880 KB Output is correct
21 Correct 5 ms 10840 KB Output is correct
22 Correct 5 ms 10892 KB Output is correct
23 Correct 5 ms 10840 KB Output is correct
24 Correct 5 ms 10840 KB Output is correct
25 Correct 4 ms 10328 KB Output is correct
26 Correct 4 ms 10840 KB Output is correct
27 Correct 5 ms 10908 KB Output is correct
28 Correct 5 ms 10840 KB Output is correct
29 Correct 4 ms 10744 KB Output is correct
30 Correct 5 ms 11036 KB Output is correct
31 Correct 5 ms 10840 KB Output is correct
32 Correct 5 ms 10840 KB Output is correct
33 Correct 4 ms 10840 KB Output is correct
34 Correct 4 ms 10840 KB Output is correct
35 Correct 4 ms 10852 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10072 KB Output is correct
2 Correct 5 ms 10840 KB Output is correct
3 Correct 5 ms 10840 KB Output is correct
4 Correct 4 ms 10840 KB Output is correct
5 Correct 5 ms 10840 KB Output is correct
6 Correct 5 ms 10840 KB Output is correct
7 Correct 4 ms 10840 KB Output is correct
8 Correct 5 ms 10840 KB Output is correct
9 Correct 4 ms 10840 KB Output is correct
10 Correct 4 ms 10840 KB Output is correct
11 Correct 4 ms 10840 KB Output is correct
12 Correct 3 ms 9904 KB Output is correct
13 Correct 6 ms 11096 KB Output is correct
14 Correct 4 ms 10872 KB Output is correct
15 Correct 6 ms 10840 KB Output is correct
16 Correct 5 ms 10820 KB Output is correct
17 Correct 4 ms 10840 KB Output is correct
18 Correct 6 ms 10816 KB Output is correct
19 Correct 5 ms 10840 KB Output is correct
20 Correct 4 ms 10880 KB Output is correct
21 Correct 5 ms 10840 KB Output is correct
22 Correct 5 ms 10892 KB Output is correct
23 Correct 5 ms 10840 KB Output is correct
24 Correct 5 ms 10840 KB Output is correct
25 Correct 4 ms 10328 KB Output is correct
26 Correct 4 ms 10840 KB Output is correct
27 Correct 5 ms 10908 KB Output is correct
28 Correct 5 ms 10840 KB Output is correct
29 Correct 4 ms 10744 KB Output is correct
30 Correct 5 ms 11036 KB Output is correct
31 Correct 5 ms 10840 KB Output is correct
32 Correct 5 ms 10840 KB Output is correct
33 Correct 4 ms 10840 KB Output is correct
34 Correct 4 ms 10840 KB Output is correct
35 Correct 4 ms 10852 KB Output is correct
36 Correct 45 ms 39504 KB Output is correct
37 Correct 72 ms 55732 KB Output is correct
38 Correct 67 ms 55788 KB Output is correct
39 Correct 65 ms 55760 KB Output is correct
40 Correct 67 ms 55752 KB Output is correct
41 Correct 66 ms 55740 KB Output is correct
42 Correct 64 ms 55784 KB Output is correct
43 Correct 57 ms 55828 KB Output is correct
44 Correct 58 ms 55768 KB Output is correct
45 Correct 57 ms 55808 KB Output is correct
46 Correct 59 ms 55888 KB Output is correct
47 Correct 64 ms 55736 KB Output is correct
48 Correct 63 ms 55856 KB Output is correct
49 Correct 63 ms 55904 KB Output is correct
50 Correct 57 ms 55760 KB Output is correct
51 Correct 58 ms 55756 KB Output is correct
52 Correct 74 ms 55964 KB Output is correct
53 Correct 64 ms 55888 KB Output is correct
54 Correct 64 ms 55868 KB Output is correct
55 Correct 58 ms 55848 KB Output is correct
56 Correct 57 ms 55888 KB Output is correct
57 Correct 67 ms 54352 KB Output is correct
58 Correct 68 ms 55744 KB Output is correct
59 Correct 64 ms 55892 KB Output is correct
60 Correct 64 ms 55756 KB Output is correct
61 Correct 63 ms 55656 KB Output is correct
62 Correct 63 ms 55988 KB Output is correct
63 Correct 64 ms 55756 KB Output is correct
64 Correct 58 ms 55736 KB Output is correct
65 Correct 58 ms 55712 KB Output is correct
66 Correct 57 ms 55736 KB Output is correct
67 Correct 56 ms 55888 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 558 ms 55480 KB Output is correct
2 Correct 780 ms 55720 KB Output is correct
3 Correct 758 ms 55772 KB Output is correct
4 Correct 704 ms 55752 KB Output is correct
5 Correct 710 ms 55880 KB Output is correct
6 Correct 681 ms 55744 KB Output is correct
7 Correct 672 ms 55756 KB Output is correct
8 Correct 686 ms 55884 KB Output is correct
9 Correct 652 ms 55764 KB Output is correct
10 Correct 693 ms 55760 KB Output is correct
11 Correct 710 ms 55772 KB Output is correct
12 Correct 659 ms 55756 KB Output is correct
13 Correct 637 ms 55856 KB Output is correct
14 Correct 4 ms 9816 KB Output is correct
15 Correct 5 ms 10840 KB Output is correct
16 Correct 4 ms 10840 KB Output is correct
17 Correct 65 ms 55744 KB Output is correct
18 Correct 65 ms 56000 KB Output is correct
19 Correct 63 ms 55812 KB Output is correct
20 Correct 57 ms 55736 KB Output is correct
21 Correct 59 ms 55748 KB Output is correct
22 Correct 65 ms 55804 KB Output is correct
23 Correct 64 ms 55692 KB Output is correct
24 Correct 65 ms 55756 KB Output is correct
25 Correct 59 ms 55744 KB Output is correct
26 Correct 58 ms 55888 KB Output is correct
27 Correct 7 ms 11252 KB Output is correct
28 Correct 4 ms 10840 KB Output is correct
29 Correct 5 ms 10840 KB Output is correct
30 Correct 5 ms 10840 KB Output is correct
31 Correct 5 ms 10840 KB Output is correct
32 Correct 5 ms 10840 KB Output is correct
33 Correct 5 ms 10840 KB Output is correct
34 Correct 5 ms 10840 KB Output is correct
35 Correct 5 ms 10840 KB Output is correct
36 Correct 4 ms 10672 KB Output is correct

Subtask #5
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 190 ms 20576 KB Output is correct
2 Correct 688 ms 55756 KB Output is correct
3 Correct 691 ms 55852 KB Output is correct
4 Correct 669 ms 55736 KB Output is correct
5 Correct 723 ms 55756 KB Output is correct
6 Correct 662 ms 55756 KB Output is correct
7 Correct 661 ms 55752 KB Output is correct
8 Correct 641 ms 55752 KB Output is correct
9 Correct 597 ms 55736 KB Output is correct
10 Correct 611 ms 55760 KB Output is correct
11 Correct 572 ms 55888 KB Output is correct
12 Correct 65 ms 55876 KB Output is correct
13 Correct 65 ms 55888 KB Output is correct
14 Correct 63 ms 55756 KB Output is correct
15 Correct 56 ms 55756 KB Output is correct
16 Correct 59 ms 55888 KB Output is correct
17 Correct 65 ms 54328 KB Output is correct
18 Correct 64 ms 55888 KB Output is correct
19 Correct 63 ms 55892 KB Output is correct
20 Correct 63 ms 55740 KB Output is correct
21 Correct 62 ms 55888 KB Output is correct
22 Correct 64 ms 55780 KB Output is correct
23 Correct 67 ms 55836 KB Output is correct
24 Correct 58 ms 55856 KB Output is correct
25 Correct 56 ms 55652 KB Output is correct
26 Correct 57 ms 55748 KB Output is correct
27 Correct 57 ms 55888 KB Output is correct
28 Correct 4 ms 10840 KB Output is correct
29 Correct 5 ms 10840 KB Output is correct
30 Correct 5 ms 10840 KB Output is correct
31 Correct 5 ms 10840 KB Output is correct
32 Correct 4 ms 10840 KB Output is correct
33 Correct 4 ms 10328 KB Output is correct
34 Correct 4 ms 10840 KB Output is correct
35 Correct 5 ms 10840 KB Output is correct
36 Correct 5 ms 10840 KB Output is correct
37 Correct 5 ms 10840 KB Output is correct
38 Correct 5 ms 10840 KB Output is correct
39 Correct 5 ms 10836 KB Output is correct
40 Correct 5 ms 10840 KB Output is correct
41 Correct 4 ms 11096 KB Output is correct
42 Correct 5 ms 10840 KB Output is correct
43 Correct 5 ms 10840 KB Output is correct

Subtask #6
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10072 KB Output is correct
2 Correct 5 ms 10840 KB Output is correct
3 Correct 5 ms 10840 KB Output is correct
4 Correct 4 ms 10840 KB Output is correct
5 Correct 5 ms 10840 KB Output is correct
6 Correct 5 ms 10840 KB Output is correct
7 Correct 4 ms 10840 KB Output is correct
8 Correct 5 ms 10840 KB Output is correct
9 Correct 4 ms 10840 KB Output is correct
10 Correct 4 ms 10840 KB Output is correct
11 Correct 4 ms 10840 KB Output is correct
12 Correct 3 ms 9904 KB Output is correct
13 Correct 6 ms 11096 KB Output is correct
14 Correct 4 ms 10872 KB Output is correct
15 Correct 6 ms 10840 KB Output is correct
16 Correct 5 ms 10820 KB Output is correct
17 Correct 4 ms 10840 KB Output is correct
18 Correct 6 ms 10816 KB Output is correct
19 Correct 5 ms 10840 KB Output is correct
20 Correct 4 ms 10880 KB Output is correct
21 Correct 5 ms 10840 KB Output is correct
22 Correct 5 ms 10892 KB Output is correct
23 Correct 5 ms 10840 KB Output is correct
24 Correct 5 ms 10840 KB Output is correct
25 Correct 4 ms 10328 KB Output is correct
26 Correct 4 ms 10840 KB Output is correct
27 Correct 5 ms 10908 KB Output is correct
28 Correct 5 ms 10840 KB Output is correct
29 Correct 4 ms 10744 KB Output is correct
30 Correct 5 ms 11036 KB Output is correct
31 Correct 5 ms 10840 KB Output is correct
32 Correct 5 ms 10840 KB Output is correct
33 Correct 4 ms 10840 KB Output is correct
34 Correct 4 ms 10840 KB Output is correct
35 Correct 4 ms 10852 KB Output is correct
36 Correct 45 ms 39504 KB Output is correct
37 Correct 72 ms 55732 KB Output is correct
38 Correct 67 ms 55788 KB Output is correct
39 Correct 65 ms 55760 KB Output is correct
40 Correct 67 ms 55752 KB Output is correct
41 Correct 66 ms 55740 KB Output is correct
42 Correct 64 ms 55784 KB Output is correct
43 Correct 57 ms 55828 KB Output is correct
44 Correct 58 ms 55768 KB Output is correct
45 Correct 57 ms 55808 KB Output is correct
46 Correct 59 ms 55888 KB Output is correct
47 Correct 64 ms 55736 KB Output is correct
48 Correct 63 ms 55856 KB Output is correct
49 Correct 63 ms 55904 KB Output is correct
50 Correct 57 ms 55760 KB Output is correct
51 Correct 58 ms 55756 KB Output is correct
52 Correct 74 ms 55964 KB Output is correct
53 Correct 64 ms 55888 KB Output is correct
54 Correct 64 ms 55868 KB Output is correct
55 Correct 58 ms 55848 KB Output is correct
56 Correct 57 ms 55888 KB Output is correct
57 Correct 67 ms 54352 KB Output is correct
58 Correct 68 ms 55744 KB Output is correct
59 Correct 64 ms 55892 KB Output is correct
60 Correct 64 ms 55756 KB Output is correct
61 Correct 63 ms 55656 KB Output is correct
62 Correct 63 ms 55988 KB Output is correct
63 Correct 64 ms 55756 KB Output is correct
64 Correct 58 ms 55736 KB Output is correct
65 Correct 58 ms 55712 KB Output is correct
66 Correct 57 ms 55736 KB Output is correct
67 Correct 56 ms 55888 KB Output is correct
68 Correct 558 ms 55480 KB Output is correct
69 Correct 780 ms 55720 KB Output is correct
70 Correct 758 ms 55772 KB Output is correct
71 Correct 704 ms 55752 KB Output is correct
72 Correct 710 ms 55880 KB Output is correct
73 Correct 681 ms 55744 KB Output is correct
74 Correct 672 ms 55756 KB Output is correct
75 Correct 686 ms 55884 KB Output is correct
76 Correct 652 ms 55764 KB Output is correct
77 Correct 693 ms 55760 KB Output is correct
78 Correct 710 ms 55772 KB Output is correct
79 Correct 659 ms 55756 KB Output is correct
80 Correct 637 ms 55856 KB Output is correct
81 Correct 4 ms 9816 KB Output is correct
82 Correct 5 ms 10840 KB Output is correct
83 Correct 4 ms 10840 KB Output is correct
84 Correct 65 ms 55744 KB Output is correct
85 Correct 65 ms 56000 KB Output is correct
86 Correct 63 ms 55812 KB Output is correct
87 Correct 57 ms 55736 KB Output is correct
88 Correct 59 ms 55748 KB Output is correct
89 Correct 65 ms 55804 KB Output is correct
90 Correct 64 ms 55692 KB Output is correct
91 Correct 65 ms 55756 KB Output is correct
92 Correct 59 ms 55744 KB Output is correct
93 Correct 58 ms 55888 KB Output is correct
94 Correct 7 ms 11252 KB Output is correct
95 Correct 4 ms 10840 KB Output is correct
96 Correct 5 ms 10840 KB Output is correct
97 Correct 5 ms 10840 KB Output is correct
98 Correct 5 ms 10840 KB Output is correct
99 Correct 5 ms 10840 KB Output is correct
100 Correct 5 ms 10840 KB Output is correct
101 Correct 5 ms 10840 KB Output is correct
102 Correct 5 ms 10840 KB Output is correct
103 Correct 4 ms 10672 KB Output is correct
104 Correct 693 ms 50508 KB Output is correct
105 Correct 781 ms 55760 KB Output is correct
106 Correct 746 ms 55740 KB Output is correct
107 Correct 726 ms 55756 KB Output is correct
108 Correct 692 ms 55868 KB Output is correct
109 Correct 762 ms 55740 KB Output is correct
110 Correct 719 ms 55736 KB Output is correct
111 Correct 654 ms 55756 KB Output is correct
112 Correct 729 ms 55744 KB Output is correct
113 Correct 667 ms 55888 KB Output is correct
114 Correct 732 ms 55680 KB Output is correct

Subtask #7
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 308 ms 36952 KB Output is correct
2 Correct 688 ms 55752 KB Output is correct
3 Correct 678 ms 55760 KB Output is correct
4 Correct 625 ms 55760 KB Output is correct
5 Correct 646 ms 55888 KB Output is correct
6 Correct 641 ms 55888 KB Output is correct
7 Correct 610 ms 55756 KB Output is correct
8 Correct 3 ms 9816 KB Output is correct
9 Correct 4 ms 10840 KB Output is correct
10 Correct 4 ms 10824 KB Output is correct
11 Correct 4 ms 10072 KB Output is correct
12 Correct 5 ms 10840 KB Output is correct
13 Correct 5 ms 10840 KB Output is correct
14 Correct 4 ms 10840 KB Output is correct
15 Correct 5 ms 10840 KB Output is correct
16 Correct 5 ms 10840 KB Output is correct
17 Correct 4 ms 10840 KB Output is correct
18 Correct 5 ms 10840 KB Output is correct
19 Correct 4 ms 10840 KB Output is correct
20 Correct 4 ms 10840 KB Output is correct
21 Correct 4 ms 10840 KB Output is correct
22 Correct 3 ms 9904 KB Output is correct
23 Correct 6 ms 11096 KB Output is correct
24 Correct 4 ms 10872 KB Output is correct
25 Correct 6 ms 10840 KB Output is correct
26 Correct 5 ms 10820 KB Output is correct
27 Correct 4 ms 10840 KB Output is correct
28 Correct 6 ms 10816 KB Output is correct
29 Correct 5 ms 10840 KB Output is correct
30 Correct 4 ms 10880 KB Output is correct
31 Correct 5 ms 10840 KB Output is correct
32 Correct 5 ms 10892 KB Output is correct
33 Correct 5 ms 10840 KB Output is correct
34 Correct 5 ms 10840 KB Output is correct
35 Correct 4 ms 10328 KB Output is correct
36 Correct 4 ms 10840 KB Output is correct
37 Correct 5 ms 10908 KB Output is correct
38 Correct 5 ms 10840 KB Output is correct
39 Correct 4 ms 10744 KB Output is correct
40 Correct 5 ms 11036 KB Output is correct
41 Correct 5 ms 10840 KB Output is correct
42 Correct 5 ms 10840 KB Output is correct
43 Correct 4 ms 10840 KB Output is correct
44 Correct 4 ms 10840 KB Output is correct
45 Correct 4 ms 10852 KB Output is correct
46 Correct 45 ms 39504 KB Output is correct
47 Correct 72 ms 55732 KB Output is correct
48 Correct 67 ms 55788 KB Output is correct
49 Correct 65 ms 55760 KB Output is correct
50 Correct 67 ms 55752 KB Output is correct
51 Correct 66 ms 55740 KB Output is correct
52 Correct 64 ms 55784 KB Output is correct
53 Correct 57 ms 55828 KB Output is correct
54 Correct 58 ms 55768 KB Output is correct
55 Correct 57 ms 55808 KB Output is correct
56 Correct 59 ms 55888 KB Output is correct
57 Correct 64 ms 55736 KB Output is correct
58 Correct 63 ms 55856 KB Output is correct
59 Correct 63 ms 55904 KB Output is correct
60 Correct 57 ms 55760 KB Output is correct
61 Correct 58 ms 55756 KB Output is correct
62 Correct 74 ms 55964 KB Output is correct
63 Correct 64 ms 55888 KB Output is correct
64 Correct 64 ms 55868 KB Output is correct
65 Correct 58 ms 55848 KB Output is correct
66 Correct 57 ms 55888 KB Output is correct
67 Correct 67 ms 54352 KB Output is correct
68 Correct 68 ms 55744 KB Output is correct
69 Correct 64 ms 55892 KB Output is correct
70 Correct 64 ms 55756 KB Output is correct
71 Correct 63 ms 55656 KB Output is correct
72 Correct 63 ms 55988 KB Output is correct
73 Correct 64 ms 55756 KB Output is correct
74 Correct 58 ms 55736 KB Output is correct
75 Correct 58 ms 55712 KB Output is correct
76 Correct 57 ms 55736 KB Output is correct
77 Correct 56 ms 55888 KB Output is correct
78 Correct 558 ms 55480 KB Output is correct
79 Correct 780 ms 55720 KB Output is correct
80 Correct 758 ms 55772 KB Output is correct
81 Correct 704 ms 55752 KB Output is correct
82 Correct 710 ms 55880 KB Output is correct
83 Correct 681 ms 55744 KB Output is correct
84 Correct 672 ms 55756 KB Output is correct
85 Correct 686 ms 55884 KB Output is correct
86 Correct 652 ms 55764 KB Output is correct
87 Correct 693 ms 55760 KB Output is correct
88 Correct 710 ms 55772 KB Output is correct
89 Correct 659 ms 55756 KB Output is correct
90 Correct 637 ms 55856 KB Output is correct
91 Correct 4 ms 9816 KB Output is correct
92 Correct 5 ms 10840 KB Output is correct
93 Correct 4 ms 10840 KB Output is correct
94 Correct 65 ms 55744 KB Output is correct
95 Correct 65 ms 56000 KB Output is correct
96 Correct 63 ms 55812 KB Output is correct
97 Correct 57 ms 55736 KB Output is correct
98 Correct 59 ms 55748 KB Output is correct
99 Correct 65 ms 55804 KB Output is correct
100 Correct 64 ms 55692 KB Output is correct
101 Correct 65 ms 55756 KB Output is correct
102 Correct 59 ms 55744 KB Output is correct
103 Correct 58 ms 55888 KB Output is correct
104 Correct 7 ms 11252 KB Output is correct
105 Correct 4 ms 10840 KB Output is correct
106 Correct 5 ms 10840 KB Output is correct
107 Correct 5 ms 10840 KB Output is correct
108 Correct 5 ms 10840 KB Output is correct
109 Correct 5 ms 10840 KB Output is correct
110 Correct 5 ms 10840 KB Output is correct
111 Correct 5 ms 10840 KB Output is correct
112 Correct 5 ms 10840 KB Output is correct
113 Correct 4 ms 10672 KB Output is correct
114 Correct 190 ms 20576 KB Output is correct
115 Correct 688 ms 55756 KB Output is correct
116 Correct 691 ms 55852 KB Output is correct
117 Correct 669 ms 55736 KB Output is correct
118 Correct 723 ms 55756 KB Output is correct
119 Correct 662 ms 55756 KB Output is correct
120 Correct 661 ms 55752 KB Output is correct
121 Correct 641 ms 55752 KB Output is correct
122 Correct 597 ms 55736 KB Output is correct
123 Correct 611 ms 55760 KB Output is correct
124 Correct 572 ms 55888 KB Output is correct
125 Correct 65 ms 55876 KB Output is correct
126 Correct 65 ms 55888 KB Output is correct
127 Correct 63 ms 55756 KB Output is correct
128 Correct 56 ms 55756 KB Output is correct
129 Correct 59 ms 55888 KB Output is correct
130 Correct 65 ms 54328 KB Output is correct
131 Correct 64 ms 55888 KB Output is correct
132 Correct 63 ms 55892 KB Output is correct
133 Correct 63 ms 55740 KB Output is correct
134 Correct 62 ms 55888 KB Output is correct
135 Correct 64 ms 55780 KB Output is correct
136 Correct 67 ms 55836 KB Output is correct
137 Correct 58 ms 55856 KB Output is correct
138 Correct 56 ms 55652 KB Output is correct
139 Correct 57 ms 55748 KB Output is correct
140 Correct 57 ms 55888 KB Output is correct
141 Correct 4 ms 10840 KB Output is correct
142 Correct 5 ms 10840 KB Output is correct
143 Correct 5 ms 10840 KB Output is correct
144 Correct 5 ms 10840 KB Output is correct
145 Correct 4 ms 10840 KB Output is correct
146 Correct 4 ms 10328 KB Output is correct
147 Correct 4 ms 10840 KB Output is correct
148 Correct 5 ms 10840 KB Output is correct
149 Correct 5 ms 10840 KB Output is correct
150 Correct 5 ms 10840 KB Output is correct
151 Correct 5 ms 10840 KB Output is correct
152 Correct 5 ms 10836 KB Output is correct
153 Correct 5 ms 10840 KB Output is correct
154 Correct 4 ms 11096 KB Output is correct
155 Correct 5 ms 10840 KB Output is correct
156 Correct 5 ms 10840 KB Output is correct
157 Correct 693 ms 50508 KB Output is correct
158 Correct 781 ms 55760 KB Output is correct
159 Correct 746 ms 55740 KB Output is correct
160 Correct 726 ms 55756 KB Output is correct
161 Correct 692 ms 55868 KB Output is correct
162 Correct 762 ms 55740 KB Output is correct
163 Correct 719 ms 55736 KB Output is correct
164 Correct 654 ms 55756 KB Output is correct
165 Correct 729 ms 55744 KB Output is correct
166 Correct 667 ms 55888 KB Output is correct
167 Correct 732 ms 55680 KB Output is correct
168 Correct 3 ms 9816 KB Output is correct
169 Correct 470 ms 25460 KB Output is correct
170 Correct 798 ms 55912 KB Output is correct
171 Correct 796 ms 55888 KB Output is correct
172 Correct 784 ms 55820 KB Output is correct
173 Correct 812 ms 55888 KB Output is correct
174 Correct 811 ms 55668 KB Output is correct
175 Correct 784 ms 55888 KB Output is correct
176 Correct 624 ms 55740 KB Output is correct
177 Correct 694 ms 55752 KB Output is correct
178 Correct 672 ms 55756 KB Output is correct
179 Correct 663 ms 55820 KB Output is correct