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: Accepted)

#include <stdio.h>
#include <stdlib.h>

int main()
{
	int i, j, c[4][4] = {};
	for (i = 1; i <= 3; i++) {
		for (j = 1; j <= 3; j++) scanf("%d", &(c[i][j]));
	}
	
	int flag = 1;
	if (c[1][1] + c[2][2] != c[1][2] + c[2][1]) flag = 0;
	if (c[1][2] + c[2][3] != c[1][3] + c[2][2]) flag = 0;
	if (c[2][1] + c[3][2] != c[2][2] + c[3][1]) flag = 0;
	if (c[2][2] + c[3][3] != c[2][3] + c[3][2]) flag = 0; 
	
	if (flag == 1) printf("Yes\n");
	else printf("No\n");
	fflush(stdout);
	return 0;
}