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;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.TreeMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;

class Main{
    static double mod = 1e9+7;

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        Library lib = new Library();
        int[][] c = new int[3][3];
        int[] rate = new int[2];
        for (int i=0;i<3;i++){
            for (int j=0;j<3;j++){
                c[i][j] = sc.nextInt();
            }
        }
        for (int i=1;i<3;i++){
            rate[i-1] = c[0][i] - c[0][i-1];
        }
        for (int i=1;i<3;i++){
            for (int j=1;j<3;j++){
                if (c[i][j]-c[i][j-1]!=rate[j-1]){
                    System.out.println("No");
                    return;
                }
            }
        }
        for (int i=1;i<3;i++){
            rate[i-1] = c[i][0] - c[i-1][0];
        }
        for (int i=1;i<3;i++){
            for (int j=1;j<3;j++){
                if (c[j][i]-c[j-1][i]!=rate[j-1]){
                    System.out.println("N0");
                    return;
                }
            }
        }
        System.out.println("Yes");
    }
}

class Library{
    static long a;
    static long b;

    public static long gcd(long a,long b){
        Library lib = new Library();
        if (a<b){
            lib.swap(a,b);
        }
        if (b==0){
            return a;
        } else {
            return gcd(b,a%b);
        }
    }

    public static void swap(long a,long b){
        long x = a;
        a = b;
        b = x;
        return;
    }
}