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>

int main(){
		int c[3][3],i,j,ab[2][3][2];
		for(i=0;i<3;i++){
				for(j=0;j<3;j++)scanf("%d",&c[i][j]);
		}
		for(i=0;i<3;i++){
				ab[0][i][0]=c[i][0]-c[i][1];
				ab[0][i][1]=c[i][1]-c[i][2];
		}
		for(i=0;i<3;i++){
				ab[1][i][0]=c[0][i]-c[1][i];
				ab[1][i][1]=c[1][i]-c[2][i];
		}
		if(ab[0][0][0]==ab[0][1][0]&&ab[0][1][0]==ab[0][2][0]&&
		ab[0][0][1]==ab[0][1][1]&&ab[0][1][1]==ab[0][2][1]&&
		ab[1][0][0]==ab[1][1][0]&&ab[1][1][0]==ab[1][2][0]&&
		ab[1][0][1]==ab[1][1][1]&&ab[1][1][1]==ab[1][2][1]){
				puts("Yes");
				return 0;
		}
		puts("No");
		return 0;
}