Problem:
Score: 300 points

Problem Statement

We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.

Constraints

c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

Sample Input 1

1 0 1
2 1 2
1 0 1

Sample Output 1

Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Sample Input 2

2 2 2
2 1 2
2 2 2

Sample Output 2

No

Takahashi is incorrect in this case.

Sample Input 3

0 8 8
0 8 8
0 8 8

Sample Output 3

Yes

Sample Input 4

1 8 6
2 9 7
0 7 7

Sample Output 4

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define all(v) v.begin(), v.end()
#define rep(i, n) for (int i = 0; i < n; i++)
typedef long long ll;

int main() {
    vector<vector<int> > c(3, vector<int>(3));
    for(int i = 0; i < 3; i++){
        for(int j = 0; j < 3; j++){
            cin >> c[i][j];
        }
    }

    bool flag = false;
    for(int i = 0; i <= 100; i++){
        int b1 = c[0][0] - i;
        int b2 = c[0][1] - i;
        int b3 = c[0][2] - i;
        if(b1 < 0 || b2 < 0 || b3 < 0) continue;
        int a2b1 = c[1][0] - b1;
        int a2b2 = c[1][1] - b2;
        int a2b3 = c[1][2] - b3;
        if(a2b1 < 0 || a2b2 < 0 || a2b3 < 0) continue;
        if(a2b1 != a2b2 || a2b2 != a2b3 || a2b1 != a2b3) continue;
        int a3b1 = c[2][0] - b1;
        int a3b2 = c[2][1] - b2;
        int a3b3 = c[2][2] - b3;
        if(a3b1 < 0 || a3b2 < 0 || a3b3 < 0) continue;
        if(a3b1 != a3b2 || a3b2 != a3b3 || a3b1 != a3b3) continue;
        flag = true;
        break;
    }
    if(flag) cout << "Yes" << endl;
    else cout << "No" << endl;

}