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: Runtime Error)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#define PI 3.141592653589793
#define MOD 1000000007


int main(){
	int c[10][10];
	for(int i=1; i<=3; i++){
		scanf("%d%d%d", &c[i][1], &c[i][2], &c[i][3]);
	}
	//scanf("%d%d%d%d", &r, &g, &b, &n);
	int x[4], y[4];
	x[0] = c[1][2] - c[1][1], x[1] = c[1][3] - c[1][2];
	y[0] = c[2][1] - c[1][1], y[1] = c[3][1] - c[2][1];
	for(int i=2; i<=3; i++){
		for(int j=2; j<=3; j++){
			if(c[i][j]-c[i][j-1] != x[j-2]){
				printf("No\n");
				exit(1);
			}
			if(c[i][j]-c[i-1][j] != y[i-2]){
				printf("No\n");
				exit(1);
			}
		}
	}
	
	printf("Yes\n");
	return 0;
}