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

            // 標準入力から1行ずつ取得
            for (int i = 0; i < 3; i++) {
                input[i] = Console.ReadLine();
            }

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

            int[] a = new int[3];
            int[] b = new int[3];
            // a0を0として考える
            a[0] = 0;
            b[0] = matrix[0, 0] - 0;
            b[1] = matrix[1, 0] - 0;
            b[2] = matrix[2, 0] - 0;
            a[1] = matrix[0, 1] - b[0];
            a[2] = matrix[0, 2] - b[2];

            if(b[0] + a[0] == matrix[0, 0] && b[0] + a[1] == matrix[0, 1] && b[0] + a[2] == matrix[0, 2] &&
               b[1] + a[0] == matrix[1, 0] && b[1] + a[1] == matrix[1, 1] && b[1] + a[2] == matrix[1, 2] &&
               b[2] + a[0] == matrix[2, 0] && b[2] + a[1] == matrix[2, 1] && b[2] + a[2] == matrix[2, 2])
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
        }
    }
}