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

    for (int i = 0; i < 3; ++i) {
      string[] val = Console.ReadLine().Split();
      for (int j = 0; j < 3; ++j) {
        g[i,j] = int.Parse(val[j]);
      }
    }

    int a1max = Math.Min(g[0,0], Math.Min(g[0,1], g[0,2]));

    int[] A = new int[3];
    int[] B = new int[3];
    bool ok = false;
    while (A[0] <= a1max) {
      for (int i = 0; i < 3; ++i) {
        B[i] = g[0,i] - A[0];
      }
      A[1] = g[1,0] - B[0];
      A[2] = g[2,0] - B[0];
      if (A[1] >= 0 && A[2] >= 0) {
        ok = true;
        for (int i = 1; i < 3; ++i) {
          for (int j = 1; j < 3; ++j) {
            if (A[i] + B[j] != g[i, j]) ok = false;
          }
        }
        if (ok) break;
      }
      ++A[0];
    }

    if (ok) {
      Console.WriteLine("Yes");
    } else {
      Console.WriteLine("No");
    }
  }
}