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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var array = new int[3][];
            for (var i = 0; i < 3; i++) array[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();

            int a2 = 0, a3 = 0, b1 = 0, b2 = 0, b3 = 0;
            var end = array[0][0];

            for (var a1 = 0; a1 <= end; a1++)
            {
                b1 = array[0][0] - a1;
                b2 = array[0][1] - a1;
                b3 = array[0][2] - a1;

                a2 = array[1][0] - b1;

                if (a2 < 0 || a2 + b2 != array[1][1] || a2 + b3 != array[1][2]) continue;

                a3 = array[2][0] - b1;

                if (a3 < 0 || a3 + b2 != array[2][1] || a3 + b3 != array[2][2]) continue;

                Console.WriteLine("Yes");
                return;
            }

            Console.WriteLine("No");
        }
    }
}