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: Wrong Answer)

using System;
using System.Linq;

namespace A
{
    class Program
    {
        static void Main(string[] args)
        {
            var c1List = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var c2List = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var c3List = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            for (var a1 = 0; a1 < c1List.Max(); a1++)
            {
                for (var a2 = 0; a2 < c2List.Max(); a2++)
                {
                    for (var a3 = 0; a3 < c3List.Max(); a3++)
                    {
                        var b1 = c1List[0] - a1 == c2List[0] - a2
                            && c1List[0] - a1 == c3List[0] - a3;

                        var b2 = c1List[1] - a1 == c2List[1] - a2
                            && c1List[1] - a1 == c3List[1] - a3;

                        var b3 = c1List[2] - a1 == c2List[2] - a2
                            && c1List[2] - a1 == c3List[2] - a3;

                        if (b1 && b2 && b3)
                        {
                            Console.WriteLine("Yes");
                            return;
                        }
                    }
                }
            }

            Console.WriteLine("No");
        }

        static int SumOfDigits(int x)
        {
            var sum = 0;
            while (x > 0)
            {
                sum += x % 10;
                x /= 10;
            }

            return sum;
        }
    }
}