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;

namespace atCoder
{
    class Program
    {

        static void Main()
        {
            string[] c1 = Console.ReadLine().Split(' ');
            string[] c2 = Console.ReadLine().Split(' ');
            string[] c3 = Console.ReadLine().Split(' ');

            for (int i = 0; i <= 100; i++)
            {
                for (int j = 0; j <= 100; j++)
                {
                    for (int k = 0; k <= 100; k++)
                    {
                        int b1 = int.Parse(c1[0]) - i;
                        int b2 = int.Parse(c2[1]) - j;
                        int b3 = int.Parse(c3[2]) - k;

                        if (i + b1 == int.Parse(c1[0]) && i + b2 == int.Parse(c1[1]) && i + b3 == int.Parse(c1[2]) &&
                            j + b1 == int.Parse(c2[0]) && j + b2 == int.Parse(c2[1]) && j + b3 == int.Parse(c2[2]) &&
                            k + b1 == int.Parse(c3[0]) && k + b2 == int.Parse(c3[1]) && k + b3 == int.Parse(c3[2]))
                        {
                            Console.WriteLine("YES");

                            return;
                        }
                    }
                }
            }

            Console.WriteLine("No");
        }
    }
}