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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
        int[,] c = new int[3,3];

        for(int i=0; i<3; i++){
            string[] input = Console.ReadLine().Split(' ');
            for(int j=0; j<3; j++){
                c[i,j] = int.Parse(input[j]);
            }
        }

        bool yes = false;

        for(int a1=0; a1<=c[0,0]; a1++){
            int b1 = c[0,0] - a1;
            int b2 = c[0,1] - a1;
            int b3 = c[0,2] - a1;
            int a2 = c[1,0] - b1;
            int a3 = c[2,0] - b1;

            if(c[1,1]==a2+b2 && c[1,2]==a2+b3 && c[2,1]==a3+b2 && c[2,2]==a3+b3){
                Console.WriteLine("Yes");
                yes = true;
                break;
            }
        }
        if(!yes){
            Console.WriteLine("No");
        }
    }
}