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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            int[,] cell = new int[3, 3];
            for (int i = 0; i < 3; ++i)
            {
                string row = Console.ReadLine();
                string[] szArr = row.Split(' ');
                for (int j = 0; j < 3; ++j)
                {
                    cell[i, j] = int.Parse(szArr[j]);
                }
            }

            bool success = false;
            for( int a1 = 0; a1 <= 100; ++a1)
            {
                int b1 = cell[0, 0] - a1;
                int b2 = cell[0, 1] - a1;
                int b3 = cell[0, 2] - a1;

                int a2 = cell[1, 0] - b1;
                int a3 = cell[2, 0] - b1;

                // 矛盾が無いか確認
                if( cell[0,0] != a1 + b1) { continue; }
                if(cell[0,1] != a1 + b2) { continue; }
                if( cell[0,2] != a1 + b3) { continue; }
                if( cell[1,0] != a2 + b1) { continue; }
                if( cell[1,1] != a2 + b2) { continue; }
                if( cell[1,2] != a2 + b3) { continue; }
                if( cell[2,0] != a3 + b1) { continue; }
                if(cell[2,1] != a3 + b2) { continue; }
                if( cell[2,2] != a3 + b3) { continue; }
                success = true;
                Console.WriteLine("YES");
            }
            Console.WriteLine("NO");
        }
    }
}