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>
#include <math.h>
#include <string.h>
#include <limits.h>

int main(void) {
	int a[3], b[3];
	int c[3][3] = { 0 };
	int flag;

	for (int i = 0; i < 3; i++) {
		for (int j = 0; j < 3; j++)scanf("%d", &c[i][j]);
	}
	
	for (int i = 0; i <= 100; i++) {
		flag = 1;
		a[0] = i;
		b[0] = c[0][0] - a[0];
		b[1] = c[0][1] - a[0];
		b[2] = c[0][2] - a[0];
		a[1] = c[1][0] - b[0];
		a[2] = c[2][0] - b[0];
		for (int j = 0; j < 3; j++) {
			for (int k = 0; k < 3; k++) {
				if (c[j][k] != a[j] + b[k]) {
					flag = 0;
					break;
				}
			}
		}
		if (flag) {
			printf("Yes");
			break;
		}
		else if (i == 100)printf("No");
	}
	return 0;
}