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;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int[][] c = new int[3][3];
		for (int i = 0; i < 3; i++) {
			for (int j = 0; j < 3; j++) {
				c[i][j] = sc.nextInt();
			}
		}

		int[] a = new int[3];
		int[] b = new int[3];

		for (int i = 0; i < 3; i++) {
			int min = 100;
			for (int j = 0; j < 3; j++) {
				if (c[i][j] < min)
					min = c[i][j];
			}
			a[i] = min;
		}
		System.out.println(Arrays.toString(a)); // debug

		for (int j = 0; j < 3; j++) {
			int min = 100;
			for (int i = 0; i < 3; i++) {
				if (c[i][j] < min)
					min = c[i][j];
			}
			b[j] = min;
		}
		System.out.println(Arrays.toString(b)); // debug

		int cnt = 0;

		for (int i = 0; i < 3; i++) {
			for (int j = 0; j < 3; j++) {
				for (int k = 0; k <= a[i]; k++) {
					for (int l = 0; l <= b[j]; l++) {
						if (k + l == c[i][j])
							cnt++;
					}
				}
			}
		}
		System.out.println(cnt);

		if (cnt == 9) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}

		sc.close();

	}

}