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.Linq;
using static System.Console;

namespace For_Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            int[][] C = new int[3][];
            C[0] = ReadLine().Split(' ').Select(int.Parse).ToArray();
            C[1] = ReadLine().Split(' ').Select(int.Parse).ToArray();
            C[2] = ReadLine().Split(' ').Select(int.Parse).ToArray();

            int[] sa = new int[12];
            for(int i=0; i < 3; i++)
            {
                sa[i] = C[0][i] - C[1][i];
                sa[i + 3] = C[1][i] - C[2][i];
                sa[i + 6] = C[i][0] - C[i][1];
                sa[i + 9] = C[i][1] - C[i][2];
            }

            string ans = "Yes";
            for(int i = 0; i < 4; i++)
            {
                if (((sa[i * 3] == sa[i * 3 + 1]) & (sa[i * 3 + 1] == sa[i * 3 + 2])) == false)
                {
                    ans = "No";
                }
            }
            WriteLine(ans);
        }
    }
}