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;

public class Hello
{
    public static void Main()
    {
        var map = new int[3, 3];
        for (int i = 0; i < 3; i++)
        {
            string[] line = Console.ReadLine().Trim().Split(' ');
            for (int j = 0; j < 3; j++)
                map[i, j] = int.Parse(line[j]);
        }
        var a = new int[3];
        var b = new int[3];
        var t = map[0, 0];
        for (int i = 0; i <= t; i++)
        {
            b[0] = map[0, 0] - i;
            b[1] = map[0, 1] - i;
            b[2] = map[0, 2] - i;
            a[0] = map[0, 0] - b[0];
            a[1] = map[1, 0] - b[0];
            a[2] = map[2, 0] - b[0];
            if (check(a, b, map)) { Console.WriteLine("Yes"); goto end; }
        }
        Console.WriteLine("No");
        end:;
    }
    public static bool check(int[] a, int[] b, int[,] map)
    {
        for (int i = 0; i < 3; i++)
            for (int j = 0; j < 3; j++)
                if (map[i, j] != a[i] + b[j]) return false;
        return true;
    }
}