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: Accepted)

import java.util.*;
import java.lang.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		int[][] cc = new int[4][4];
		for( int i=1; i<=3; i++ ){
			for( int k=1; k<=3; k++ ){
				cc[i][k] = sc.nextInt();
			}
		}
		loop:for( int i=0; i<=100; i++ ){
			for( int j=0; j<=100; j++ ){
				for( int k=0; k<=100; k++ ){
					int a = cc[1][1]-i;
					int b = cc[1][2]-i;
					int c = cc[1][3]-i;
					int d = cc[2][1]-j;
					int e = cc[2][2]-j;
					int f = cc[2][3]-j;
					int g = cc[3][1]-k;
					int h = cc[3][2]-k;
					int l = cc[3][3]-k;
					if( a==d && d==g && b==e && e==h && c==f && f==l ){
						System.out.println("Yes");
						break loop;
					}
				}
			}
			if( i==100 ){
				System.out.println("No");
				break;
			}
		}
	}
}