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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Map;
import java.util.HashMap;
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        int a1, a2, a3, b1, b2, b3;
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int[][] grid = new int[3][3];
        String ans = "No";
        
        for (int i = 0; i < 3; i++) {
            String[] line = br.readLine().split(" ");
            for (int j = 0; j < 3; j++) {
                grid[i][j] = Integer.parseInt(line[j]);
            }
        }
        
        for (a1 = 0; a1 <= grid[0][0]; a1++) {
            b1 = grid[0][0] - a1;
            b2 = grid[0][1] - a1;
            b3 = grid[0][2] - a1;
            a2 = grid[1][0] - b1;
            a3 = grid[2][0] - b1;
            if (a2 + b2 == grid[1][1] && a2 + b3 == grid[1][2] && a3 + b2 == grid[2][1] && a3 + b3 == grid[2][2]) ans = "Yes";
        }
        
        
        System.out.println(ans);
    }
}