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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int[][] a = new int[3][3];
		for(int i = 0 ; i < 3 ; i++) {
			for(int j = 0 ; j < 3 ; j++) {
				a[i][j] = sc.nextInt();
			}
		}
		// a0とa1とa2を固定
		for(int i = -100 ; i <= 100 ; i++) {
			for(int j = -100 ; j <= 100 ; j++) {
				for(int k = -100 ; k <= 100 ; k++) {
					int b0 = a[0][0] - i;
					int b1 = a[0][1] - i;
					int b2 = a[0][2] - i;
					if(j + b1 == a[1][1] && j + b2 == a[1][2] && k + b1 == a[2][1] && k + b2 == a[2][2]) {
						if(0 <= i + b0 && i + b0 <= 100 && 0 <= i + b1 && i + b1 <= 100 && 0 <= i + b2 && i + b2 <= 100 && 0 <= j + b0 && j + b0 <= 100 && 0 <= k + b0 && k + b0 <= 100 && 0 <= j + b1 && j + b1 <= 100 && 0 <= k + b1 && k + b1 <= 100 && 0 <= j + b2 && j + b2 <= 100 && 0 <= k + b2 && k + b2 <= 100) {
							System.out.println("Yes");
							return;
						}
					}
				}
			}
		}
		System.out.println("No");
	}
}