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

class Program
{
    static void Main(string[] args)
    {
        // 入力
        int[][] jag = new int[3][];
        for (int i = 0; i < 3; i++)
        {
            jag[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();
        }

        string ans = "Yes";
        //a1+a2
        if (jag[0][0] - jag[1][0] != jag[0][1] - jag[1][1] || jag[0][0] - jag[1][0] != jag[0][2] - jag[1][2])
        {
            ans = "No";
        }
        //a2+a3
        if (jag[1][0] - jag[2][0] != jag[1][1] - jag[2][1] || jag[1][0] - jag[2][0] != jag[1][2] - jag[2][2])
        {
            ans = "No";
        }
        //a3+a1
        if (jag[0][0] - jag[2][0] != jag[0][1] - jag[2][1] || jag[0][0] - jag[2][0] != jag[0][2] - jag[2][2])
        {
            ans = "No";
        }

        //b1+b2
        if (jag[0][0] - jag[0][1] != jag[1][0] - jag[1][1] || jag[0][0] - jag[0][1] != jag[2][0] - jag[2][1])
        {
            ans = "No";
        }
        //b2+b3
        if (jag[0][1] - jag[0][2] != jag[1][1] - jag[1][2] || jag[0][1] - jag[0][2] != jag[2][1] - jag[2][2])
        {
            ans = "No";
        }
        //b3+b1
        if (jag[0][0] - jag[0][2] != jag[1][0] - jag[1][2] || jag[0][0] - jag[0][2] != jag[2][0] - jag[2][2])
        {
            ans = "No";
        }
        Console.WriteLine(ans);


    }
}