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>
typedef long long ll;
#define sz(x) int(x.size())
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;

int main(void){
    int c[4][4];
    for (int i = 0; i < 3; i++)
    {
        for (int j = 0; j < 3; j++)
        {
            int a;
            cin >> a;
            c[i+1][j+1] = a;
        }
    }
    if(c[1][3] - c[1][2] == c[2][3]-c[2][2] && c[3][3] - c[3][2] == c[2][3]-c[2][2]){
        if(c[1][2] - c[1][1] == c[2][2]-c[2][1] && c[3][2] - c[3][1] == c[2][2]-c[2][1]){
            if(c[3][3]-c[2][3] == c[3][2]-c[2][2] && c[3][2]-c[2][2] == c[3][1]-c[2][1]){
                if(c[2][3]-c[1][3] == c[2][2]-c[1][2] && c[2][2]-c[1][2] == c[2][1]-c[1][1]){
                    cout << "Yes" << endl;
                    return 0;
                }
            }
        }
    }
    cout << "No" << endl;
}