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.Text;
    using System.Collections.Generic;
    using static System.Math;
    using System.Linq;
    using static System.Array;
    
    namespace ConsoleApp2
    {
    class Program
    {
        static string S;
        static long ans = 0;
        static long N;
        static long M;
        static Node[] Nodes;
        static void Main(string[] args)
        {

            var map = new int[3][];
            for (int i = 0; i < 3; i++)
            {
                map[i] = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            }

            var a1 = 0;
            var b1 = map[0][0] - a1;
            var b2 = map[0][1] - a1;
            var b3 = map[0][2] - a1;
            var a2 = map[1][0] - b1;
            var a3 = map[2][0] - b1;

            if(a2+b2 == map[1][1] && a2 + b3 == map[1][2] && a3+ b2 == map[2][1] && a3 + b3 == map[2][2])
            {
                Console.WriteLine("Yes");   
            }
            else
            {
                Console.WriteLine("No");
            }
            
        }


    }

    class Node
    {
        long num = -1;
        public List<long> adj;
        public Node(long inp)
        {
            this.num = inp;
            adj = new List<long>();
        }
    }
}