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 9.2.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;
int main() {
	int c[3][3];
	int a[3];
	int b[3];
	int min;
	bool flag = false;
	for (int a = 0;a < 3;a ++) {
		for (int b = 0;b < 3;b++)
			cin >> c[a][b];
	}//数値の格納
	min = c[0][0];
	for (int d = 1;d < 3;d++) {
		if (c[0][d] < min)
			min = c[0][d];
	}//minを定義
	for (a[0] = 0;a[0] <= min;a[0]++) {
		for (int i = 0;i < 3;i++) {
			b[i] = c[0][i] - a[0];
		}
		a[1] = c[1][0] - b[0];
		a[2] = c[2][0] - b[0];
		if (a[1] + b[1] == c[1][1] && a[1] + b[2] == c[1][2] && a[2]+b[1]==c[2][1] && a[2]+b[2]==c[2][2]) {
			flag = true;
			break;
		}
		

	}
	if (flag)
		cout << "Yes";
	else cout << "No";
}