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.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        List<Integer> c1 = new ArrayList<>();
        List<Integer> c2 = new ArrayList<>();
        List<Integer> c3 = new ArrayList<>();
        IntStream.range(0, 3).forEach(i -> c1.add(sc.nextInt()));
        IntStream.range(0, 3).forEach(i -> c2.add(sc.nextInt()));
        IntStream.range(0, 3).forEach(i -> c3.add(sc.nextInt()));

        int a1 = 0;
        int b1 = c1.get(0) - a1;
        int a2 = c2.get(0) - b1;
        int b2 = c2.get(1) - a2;
        int a3 = c3.get(0) - b1;
        int b3 = c3.get(2) - a3;

        if (c1.get(0) == a1 + b1 && c1.get(1) == a1 + b2 && c1.get(2) == a1 + b3
                && c2.get(0) == a2 + b1 && c2.get(1) == a2 + b2 && c2.get(2) == a2 + b3
                && c3.get(0) == a3 + b1 && c3.get(1) == a3 + b2 && c3.get(2) == a3 + b3) {
            System.out.println("Yes");
            return;
        }
        System.out.println("No");
    }

}