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 Cmondai
{
    static void Main()
    {
        var array = new int[3,3];
        var max = int.MinValue;
        var min = int.MaxValue;
        for (int i=0;i<3;++i)
        {
            var list = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
            for (int j = 0; j < 3; ++j)
            {
                array[i, j] = list[j];
                if (max < list[j]) max = list[j];
                if (list[j] < min) min = list[j];
            }
        }
        var start = (max - min) * (-1);
        var ans = "No";
        for (int i=start;i<=max;++i)
        {
            var a1 = i;
            var b1 = array[0, 0] - a1;
            var b2 = array[0, 1] - a1;
            var b3 = array[0, 2] - a1;
            var a2 = array[1, 0] - b1;
            var a3 = array[2, 0] - b1;
            if(array[0,0]==a1+b1 && array[0,1]== a1 + b2 && array[0,2]== a1 + b3
                && array[1,0]== a2 + b1 && array[1,1]== a2 + b2 && array[1,2]== a2 + b3
                && array[2,0]== a3 + b1 && array[2,1]== a3 + b2 && array[2, 2] == a3 + b3)
            {
                ans = "Yes";
            }
                        
        }
        Console.WriteLine(ans);
    }
}