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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC088_C
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] a = new int[3];
            int[] b = new int[3];
            int[][] c = new int[3][];
            bool p = true;
            bool ans = false;
            for (int i = 0; i < 3; i++)
            {
                c[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();
            }
            for (int i = 0; i <= 100; i++)
            {
                a[0] = i;
                for (int j = 0; j <= 100; j++)
                {
                    a[1] = j;
                    for (int k = 0; k <= 100; k++)
                    {
                        for (int l = 0; l < 3; l++)
                        {
                            b = new int[3] { c[l][0] - a[0], c[l][1] - a[0], c[l][2] - a[0] };
                            for (int m = 0; m < 3; m++)
                            {

                                if (c[l][m] != a[l] + b[m]) { p = false; }
                            }
                        }
                        ans |= p;
                    }
                }
            }
            Console.WriteLine(ans ? "Yes" : "No");
        }
    }
}