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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(void){
  int c[3][3];
  int ans = 0;
  
    for(int i = 0;i < 3;i ++){
    for(int j = 0;j < 3;j ++){
      scanf("%d",&c[i][j]);
    }
  }
  
  int a[3] = {101 ,101 ,101} , b[3] = {101 ,101 ,101};
  
  for(int j = 0;j < 3;j ++){
   for(int i = 0;i < 3;i ++){
    if(a[j] > c[j][i]){
      a[j] = c[j][i];
    }
  }
 }
     
  for(int i = 0;i < 3;i ++){
    for(int j = 0;j < 3;j ++){
      if(b[i] > c[j][i]){
        b[i] = c[j][i];
      }
    }
  }
  
  for(int i = 0;i < 3;i ++){
    for(int j = 0;j < 3;j ++){
      if(a[i] + b[j] != c[i][j]){
        ans ++;
      }
    }
  }
  
 if(ans == 0){
   printf("Yes\n");
 }
 else{
   printf("No\n");
 }
 return 0;
}