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 <time.h>
typedef long long ll;
typedef long double ld;
#define INF (1LL<<60)
/*swap 交換*/
void swap(ll *a, ll *b){ll c;c=*b;*b=*a;*a=c;}
/*2つのうち大きい数を返す*/
ll max2(ll a,ll b){return a>=b?a:b;}
/*2つのうち小さい数を返す*/
ll min2(ll a,ll b){return a>=b?b:a;}
/*絶対値*/
ll ABS(ll a){return a>=0?a:(-a);}
typedef struct{
    ll aa;
    ll bb;
}frequent;
// 小大
int compare(const void *a, const void *b){return *(ll *)a - *(ll *)b;}

int main(void){
    ll i,ans=0;
    ll c[9];
    for(i=0;i<9;i++){
        scanf("%lld",&c[i]);
    }
    if( !(c[0]-c[1]==c[3]-c[4] && c[3]-c[4]==c[6]-c[7]) || !(c[2]-c[1]==c[5]-c[4] && c[5]-c[4]==c[8]-c[7]) || !(c[0]-c[3]==c[1]-c[4] && c[1]-c[4]==c[2]-c[5]) || !(c[6]-c[3]==c[7]-c[4] && c[7]-c[4]==c[8]-c[5]) ){
        ans=1;
    }
    if(ans==1) printf("No\n");
    if(ans==0) printf("Yes\n");
    return 0;
}