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.Scanner;
import java.util.Arrays;

public class Main {

public static void main(String [] args){


        int H,W,D;
        int count =0;
        Scanner input = new Scanner(System.in);
        String Ans = "Yes";
        int [][] arr = new int[4][4];

        for (int i=1; i<=3; i++ ) {
                for (int j=1; j<=3; j++ ) {
                        arr[i][j] = input.nextInt();
                }
        }

        if (arr[1][1]-arr[2][1] != arr[1][2]-arr[2][2] || arr[1][2]-arr[2][2] != arr[1][3]-arr[2][3]) {
                //a1 - a2
                Ans = "No";
        }else if (arr[2][1]-arr[3][1] != arr[2][2]-arr[3][2] || arr[2][2]-arr[3][2] != arr[2][3]-arr[3][3]) {
                //a2 - a3
                Ans = "No";
        }else if (arr[3][1]-arr[1][1] != arr[3][2]-arr[1][2] || arr[3][2]-arr[1][2] != arr[3][3]-arr[1][3]) {
                //a3 - a1
                Ans = "No";
        }else if (arr[1][1]-arr[1][2] != arr[2][1]-arr[2][2] || arr[2][1]-arr[2][2] != arr[3][1]-arr[3][2]) {
                //b1 - b2
                Ans = "No";
        }else if (arr[1][2]-arr[1][3] != arr[2][2]-arr[2][3] || arr[2][2]-arr[2][3] != arr[3][2]-arr[3][3]) {
                //b2 - b3
                Ans = "No";
        }else if (arr[1][3]-arr[1][1] != arr[2][3]-arr[2][1] || arr[2][3]-arr[2][1] != arr[3][3]-arr[3][1]) {
                //b3 - b1
                Ans = "No";
        }

        System.out.println(Ans);
}
}