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;

namespace TestApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var ls = new int[3, 3];
            for (int i = 0; i < 3; i++)
            {
                var str = Console.ReadLine()
                    .Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries)
                    .Select(x => int.Parse(x))
                    .ToArray();
                for (int j = 0; j < 3; j++)
                {
                    ls[j, i] = str[j];
                }
            }

            int c11 = ls[0, 0];
            int c12 = ls[0, 1];
            int c13 = ls[0, 2];
            int c21 = ls[1, 0];
            int c22 = ls[1, 1];
            int c23 = ls[1, 2];
            int c31 = ls[2, 0];
            int c32 = ls[2, 1];
            int c33 = ls[2, 2];
            bool isTrue = false;
            if (c11 - c12 == c21 - c22 && c21 - c22 == c31 - c32)
            {
                if (c11 - c13 == c21 - c23 && c21 - c23 == c31 - c33)
                {
                    if (c12 - c13 == c22 - c23 && c22 - c23 == c32 - c33)
                    {
                        if (c11 - c21 == c12 - c22 && c12 - c22 ==c13 - c23)
                        {
                            if (c21 - c31 == c22 - c32 && c22 - c32 == c23 - c33)
                            {
                                if (c11- c31 == c12 - c32 && c12 - c32 ==c13 - c33)
                                {
                                    isTrue = true;
                                }
                            }
                        }
                    }
                }
            }
            if (isTrue)
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
            Console.ReadLine();
        }
        
    }

}