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: Wrong Answer)

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


    class Program
    {


        static void Main(string[] args)
        {
            Solve();
        }

        static void Solve()
        {
            Scan sc = new Scan();
            write wr = new write();


            int[] c1 = sc.intarr;
            int[] c2 = sc.intarr;
            int[] c3 = sc.intarr;

            bool han = false;

            
            for(int i = 0; i < 100; ++i)
            {
                for(int j = 0; j < 100; ++j)
                {
                    for(int k = 0; k < 100; ++k)
                    {
                        if(c1[0]-i==c1[1]-j&& c1[1]-j == c1[2]-k&& c2[0] - i == c2[1] - j && c2[1] - j == c2[2] - k && c3[0] - i == c3[1] - j && c3[1] - j == c3[2] - k)
                        {
                        han = true;
                        }
                    }
                }
            }

        if (han) wr.wri("Yes");
        else wr.wri("No");
        }
}


    class Scan
    {
    public string str => Console.ReadLine();

    public string[] strarr => str.Split(' ');

    public long[] longarr => strarr.Select(long.Parse).ToArray();
    public int [] intarr => strarr.Select(int.Parse).ToArray();



}

class write
{
    public void wri<Type>(Type x)
    {
        Console.WriteLine(x);
    }
}