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;

namespace Competitive
{
    internal class Solution
    {
        private int[,] A;
        private int N;
        
        public void Run()
        {
            N = 3;
            A = new int[N, N];
            for (int i = 0; i < N; i++)
            {
                int[] ary = Input.ReadIntArray();
                for (int j = 0; j < N; j++)
                    A[i, j] = ary[j];

            }

            Console.WriteLine(Solve() ? "Yes" : "No" );

        }

        private bool Solve()
        {
            
            for (int i = 1; i < N; i++)
            {
                for(int j = 0; j < N; j++)
                    if (A[i, j] + A[0, 0] != A[0, j] + A[i, 0])
                        return false;
            }

            return true;

        }

    }

    internal static class Input
    {
        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }
    }

    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}