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)

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

#define int long long

int dx[] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[] = {0, 1, 0, -1, 1, 1, -1, -1};

int c[3][3];
signed main() {
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            cin >> c[i][j];
        }
    }
    for (int i = 0; i <= 100; i++) {
        for (int j = 0; j <= 100; j++) {
            for (int k = 0; k <= 100; k++) {
                int b1 = c[0][0] - i, b2 = c[0][1] - i, b3 = c[0][2] - i;
                if (j + b1 == c[1][0] && k + b1 == c[2][0] &&
                    j + b2 == c[1][1] && k + b2 == c[2][1] &&
                    j + b3 == c[1][2] && k + b3 == c[2][2]) {
                    cout << "Yes" << endl;
                    return 0;
                }
            }
        }
    }
    cout << "No" << endl;
    return 0;
}