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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace TInfo
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');
            int c11 = int.Parse(str[0]);
            int c12 = int.Parse(str[1]);
            int c13 = int.Parse(str[2]);

            str = Console.ReadLine().Split(' ');
            int c21 = int.Parse(str[0]);
            int c22 = int.Parse(str[1]);
            int c23 = int.Parse(str[2]);

            str = Console.ReadLine().Split(' ');
            int c31 = int.Parse(str[0]);
            int c32 = int.Parse(str[1]);
            int c33 = int.Parse(str[2]);

            int c1 = c22 - c21 - c12 + c11;
            int c2 = c32 - c31 - c12 + c11;
            int c3 = c23 - c21 - c13 + c11;
            int c4 = c33 - c31 - c13 + c11;

            if (c1 == 0 && c2 == 0 && c3 == 0 && c4 == 0)
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
        }
    }
}