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<string>
#include<vector>
#include<map>
#include<tuple>
#include<algorithm>
#include<cmath>
#include<limits>
#include<set>
#include<queue>
using namespace std;
#define int long  long int
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int lcm(int a, int b) { return a / gcd(a, b) * b; }
typedef pair<int, int>P;
const int INF = 1e8;

signed main() {
	int c[3][3];
	rep(i, 3)rep(j, 3)cin >> c[i][j];
	int num1, num2;
	rep(i, 2) {
		rep(j, 3) {
			if (!j)num1 = c[i + 1][j] - c[i][j];
			else if (num1 != c[i + 1][j]-c[i][j]) {
				cout << "No";
				return 0;
			}

			if (!j)num2 = c[j][i + 1] - c[j][i];
			else if (num2 != c[j][i + 1] - c[j][i]) {
				cout << "No";
				return 0;
			}
		}
	}
	cout << "Yes";
}