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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define REP(i,n) for(int i=0;i<(n);i++)
#define REP2(i,a,b) for(int i=(a);i<(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define INF 2e9
typedef long long ll;

int main()
{
    vector<vector<int> > c(3,vector<int>(3));
    REP(i,3) REP(j,3) cin>>c[i][j];

    bool f=0;
    // REP2(a1,-1000,1000){
        int a1=0;
        int a2,a3,b1,b2,b3;
        b1=c[0][0]-a1;b2=c[0][1]-a1;b3=c[0][2]-a1;
        a2=c[1][0]-b1;
        if(a2!=c[1][1]-b2 || a2!=c[1][2]-b3) f=0;
        else{
            a3=c[2][0]-b1;
            if(a3!=c[2][1]-b2 || a3!=c[2][2]-b3) f=0;
            else f=1;
        }
        // break;
    // }
    cout<<(f? "Yes":"No")<<endl;

	return 0; 
}