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<iostream>
#include<stdio.h>
#include<algorithm>
#include<vector>
#include<string.h>
#include<math.h>
#include<map>
#include<iomanip>

#define MOD 1e9+7;
#define INF 1e17+9;
#define PI acos(-1);

using namespace std;

int main(){
	int c[3][3];
	for(int i=0;i<3;i++){
		for(int j=0;j<3;j++){
			cin >> c[i][j];
		}
	}
	if(c[0][0]-c[0][1]==c[1][0]-c[1][1] && c[1][0]-c[1][1]==c[2][0]-c[2][1]){
		if(c[0][1]-c[0][2]==c[1][1]-c[1][2] && c[1][1]-c[1][2]==c[2][1]-c[2][2]){
			if(c[0][0]-c[0][2]==c[1][0]-c[1][2] && c[1][0]-c[1][2]==c[2][0]-c[2][2]){
				cout << "Yes" << endl;
				return 0;
			}
		}
	}
			cout << "No" << endl;
	return 0;
}