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;
using System.Threading.Tasks;

namespace AtCoderBS
{
    class Program
    {
        static void Main(string[] args)
        {
            bool Takahashi = false;
            int[] c1 = new int[3];
            int[] c2 = new int[3];
            int[] c3 = new int[3];

            int a1, a2, a3, b1, b2, b3 = 0;

            string[] str = new string[3];

            for (int i = 0; i < 3; i++)
            {
                str = Console.ReadLine().Split(' ');
                c1[i] = int.Parse(str[0]);
                c2[i] = int.Parse(str[1]);
                c3[i] = int.Parse(str[2]);
            }

            int c1Max = c1.Max();
            int c2Max = c2.Max();
            int c3Max = c3.Max();

            for (b1 = 0; b1 <= c1Max; b1++)
            {
                a1 = c1[0] - b1; // 1列目決定
                a2 = c1[1] - b1;
                a3 = c1[2] - b1;

                for (b2 = 0; b2 <= c2Max; b2++)
                {
                    if (a1 + b2 == c2[0] && a2 + b2 == c2[1] && a3 + b2 == c2[2]) // 2列目成立
                    {
                        for (b3 = 0; b3 <= c3Max; b3++)
                        {
                            if (a1 + b3 == c3[0] && a2 + b3 == c3[1] && a3 + b3 == c3[2]) // 3列目成立
                            {
                                Takahashi = true;
                                goto Fin;
                            }
                        }
                    }
                }
            }

            Fin:

            if (Takahashi)
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }
            Console.Read();
        }
    }
}