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;

public class Program
{
    static void Main()
    {
        var grid = new int[3][];
        for (int i = 0; i < 3; i++)
        {
            grid[i] = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        }

        var min = grid.Select(x => x.Min()).Min();
        grid = grid.Select(x => x.Select(y => y - min).ToArray()).ToArray();

        var a = new int[3];
        var b = new int[3];

        //全探索
        for (int i = 0; i <= 100; i++)
        {
            a[0] = i;
            for (int j = 0; j < 3; j++)
            {
                b[j] = grid[0][j] - a[0];
            }

            for (int j = 1; j < 3; j++)
            {
                a[j] = grid[j][0] - b[0];
            }

            var flag = true;
            for (int row = 0; row < 3; row++)
            {
                for (int col = 0; col < 3; col++)
                {
                    if (grid[row][col] != a[row]+b[col])
                    {
                        flag = false;
                        break;
                    }
                }
            }

            if (flag)
            {
                Console.WriteLine("Yes");
                return;
            }
        }

        Console.WriteLine("No");
    }
}