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 AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var c1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            var c2 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            var c3 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            string ans = "Yes";
            if (c1.Zip(c2, (x, y) => x - y).Distinct().Count() != 1) ans = "No";
            if (c1.Zip(c3, (x, y) => x - y).Distinct().Count() != 1) ans = "No";
            var temp = c1.ToArray();
            c1[1] = c2[0];
            c1[2] = c3[0];
            c2[0] = temp[1];
            c3[0] = temp[2];
            temp = c2.ToArray();
            c2[2] = c3[1];
            c3[1] = temp[2];
            if (c1.Zip(c2, (x, y) => x - y).Distinct().Count() != 1) ans = "No";
            if (c1.Zip(c3, (x, y) => x - y).Distinct().Count() != 1) ans = "No";
            Console.WriteLine(ans);
        }
    }
}