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.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int[][] map = new int[3][3];
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                map[i][j] = scan.nextInt();
            }
        }
        boolean found = true;
        // a1-a2
        if (map[0][0] - map[1][0] != map[0][1] - map[1][1] || map[0][1] - map[1][1] != map[0][2] - map[1][2]) {
            found = false;
        }
        // a2-a3
        if (map[1][0] - map[2][0] != map[1][1] - map[2][1] || map[1][1] - map[2][1] != map[1][2] - map[2][2]) {
            found = false;
        }
        // a3-a1
        if (map[2][0] - map[0][0] != map[2][1] - map[0][1] || map[2][1] - map[0][1] != map[2][2] - map[0][2]) {
            found = false;
        }
        // b1-b2
        if (map[0][0] - map[0][1] != map[1][0] - map[1][1] || map[1][0] - map[1][1] != map[2][0] - map[2][1]) {
            found = false;
        }
        // b2-b3
        if (map[0][1] - map[0][2] != map[1][1] - map[1][2] || map[1][1] - map[1][2] != map[2][1] - map[2][2]) {
            found = false;
        }
        // b3-b1
        if (map[2][2] - map[2][0] != map[1][2] - map[1][0] || map[1][2] - map[1][0] != map[0][2] - map[0][0]) {
            found = false;
        }
        System.out.println(found ? "Yes" : "No");
    }
}