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()
{
	int c[3][3];
	int a[3];
	int b[3];
	int i,j,k;
	int hantei = 0;
	
	for(i=0; i<3; i++){
		for(j=0; j<3; j++){
			scanf("%d",	&c[i][j]);
		}
	}
	
	for(i=0; i<c[0][0]; i++){
		while(hantei == 0){
			int sum = 0;
			a[0] = i;
			for(j=0; j<2; j++){
				b[j] = c[0][j] - i;
			}
			for(j=1; j<2; j++){
				a[j] = c[j][0] - b[0];
			}
			for(j=0; j<2; j++){
				for(k=0; k<2; k++){
					sum += c[j][k] - a[j] -b[k];
				}
		}
		if(i == c[0][0]) hantei = 0;
		if(sum == 0) hantei = 1;
		}
	}
	
	if(hantei) printf("Yes");
	else printf("No");
	
	return 0;
}