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;
using System.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;
 
class Program
 {
        static int R;

        static void Main(string[] args)
        {
          var grid = new long[3][];
          for(int i = 0; i < 3 ; i++){
            grid[i] = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
          }
          
          var flag = true;
          for(int i = 0; i < 2 ; i++){
            for(int j = i+1; j < 3 ; j++){
              
              if(grid[j][0]-grid[i][0] != grid[j][1]-grid[i][1]){
                flag = false;
              }
              
              if(grid[j][0]-grid[i][0] != grid[j][2]-grid[i][2]){
                flag = false;
              }
              
            }
          }
          
          for(int i = 0; i < 2 ; i++){
            for(int j = i+1; j < 3 ; j++){
              
              if(grid[0][j]-grid[0][i] != grid[1][j]-grid[1][i]){
                flag = false;
              }
              
              if(grid[0][j]-grid[0][i] != grid[2][j]-grid[2][i]){
                flag = false;
              }

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

          
        }
}