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 <string.h>
#include <math.h>
int main(void)
{
	int a[4][4];
	int b[4][4];
	int c[4];
	int d[4];
	int i,j;
	int k,tamp=1;
	for(i=1;i<=3;i++)
	for(j=1;j<=3;j++)
	{
		scanf("%d",&a[i][j]);
	}
	for(i=0;i<=100;i++)
	{
		c[1]=i;
		d[1]=a[1][1]-c[1];
		if(d[1]<0)
		{
			tamp=0;
			break;
		}
		c[2]=a[2][1]-d[1];
		d[2]=a[2][2]-c[2];
		c[3]=a[3][2]-d[2];
		d[3]=a[3][3]-c[3];
		for(j=1;j<=3;j++)
		for(k=1;k<=3;k++)
		{
			b[j][k]=c[j]+d[k];
			if(b[j][k]!=a[j][k])
			{
				tamp=0;
				break;
			}
		}
		if(j==4)
		break;
	}
	if(tamp==1)
	printf("Yes\n");
	else
	printf("No\n");
}