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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int main() 
{
    vector<int> c(9);
    for(int i = 0;i < 9;++i)
        cin >> c.at(i);
    bool is = false;
    int a1,a2,a3,b1,b2,b3;
    for(int i = 0;i <= 100;++i)
    {
        a1 = i;
        b1 = c[0] - a1;
        b2 = c[1] - a1;
        b3 = c[2] - a1;
        a2 = c[3] - b1;
        a3 = c[6] - b1;
        if(a1 + b1 == c[0] && a1 + b2 == c[1] && a1 + b3 == c[2] && a2 + b1 == c[3] && a2 + b2 == c[4] && a2 + b3 && a3 + b1 == c[6] && a3 + b2 == c[7] && a3 + b3 == c[8])
        {
            is = true;
        }
        
    } 
    cout << ( is ? "Yes\n" : "No\n");
}