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 (Clang 3.8.0) (judge verdict: Accepted)

#include<stdio.h>

int main(void)
{int i,j;
int c[3][3];
int a0[3],a1[3],a2[3];
for(i=0;i<3;i++)
{for(j=0;j<3;j++)
{scanf("%d",&c[i][j]);}}

a0[0]= c[0][2]-c[0][0];
a1[0]= c[1][2]-c[1][0] ;
a2[0]= c[2][2]-c[2][0];
a0[1]= c[0][2]-c[0][1] ;
a1[1]= c[1][2]-c[1][1] ;
a2[1]= c[2][2]-c[2][1];
a0[2]= c[0][1]-c[0][0] ;
a1[2]= c[1][1]-c[1][0] ;
a2[2]= c[2][1]-c[2][0];
for(i=0;i<3;i++)
{if(a0[i]!=a1[i]||a0[i]!=a2[i])
{printf("No");
return 0;}}
a0[0]= c[0][0]-c[2][0] ;
a1[0]= c[0][1]-c[2][1] ;
a2[0]= c[0][2]-c[2][2];
a0[1]= c[0][0]-c[1][0] ;
a1[1]= c[0][1]-c[1][1] ;
a2[1]= c[0][2]-c[1][2];
a0[2]= c[1][0]-c[2][0] ;
a1[2]= c[1][1]-c[2][1] ;
a2[2]= c[1][2]-c[2][2];
for(i=0;i<3;i++)
{if(a0[i]!=a1[i]||a0[i]!=a2[i])
{printf("No");
return 0;}}
printf("Yes");
return 0;
}