codeforces Wunder Fund Round 2016 (Div. 1 + Div. 2 combined) B Guess the Permutation

Posted 2020-06-11

B. Guess the Permutation

Bob has a permutation of integers from 1 to n. Denote this permutation as p. The i-th element of p will be denoted as pi. For all pairs of distinct integers i, j between 1 and n, he wrote the number ai, j = min(pi, pj). He writes ai, i = 0 for all integer i from 1 to n.

Bob gave you all the values of ai, j that he wrote down. Your job is to reconstruct any permutation that could have generated these values. The input will be formed so that it is guaranteed that there is at least one solution that is consistent with the information given.

Input

The first line of the input will contain a single integer n (2 ≤ n ≤ 50).

The next n lines will contain the values of ai, j. The j-th number on the i-th line will represent ai, j. The i-th number on the i-th line will be0. It‘s guaranteed that ai, j = aj, i and there is at least one solution consistent with the information given.

Output

Print n space separated integers, which represents a permutation that could have generated these values. If there are multiple possible solutions, print any of them.

Sample test(s)

input

2
0 1
1 0

output

2 1

input

5
0 2 2 1 2
2 0 4 1 3
2 4 0 1 3
1 1 1 0 1
2 3 3 1 0

output

2 5 4 1 3

Note

In the first case, the answer can be {1, 2} or {2, 1}.

In the second case, another possible answer is {2, 4, 5, 1, 3}.

 

/*找第i个数的位置,第i个数所在的那一行肯定不会有比它大的数,行号就是它的位置,注意标记就行了*/
#include<cstdio>
#include<cstring>
#include<map>
#include<stack>
#include<iostream>
#include<algorithm>
using namespace std;
int a[55][55],p[55];
bool vis[55];
int main()
{
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++)
            scanf("%d",&a[i][j]);
    for(int i=1;i<=n;i++)
    {
        int j;
        for(j=1;j<=n;j++)
        {
            int k;
            for(k=1;k<=n;k++)
                if(a[j][k]>i)break;
            if(k==n+1&&!vis[j])break;
        }
        vis[j]=1;
        p[j]=i;
    }
    for(int i=1;i<=n;i++)
        printf("%d ",p[i]);
    return 0;
}