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 ABC088_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var num = new double[3][];
            var input = "";
            var arrayTemp = new string[3];
            for (int i = 0; i < 3; i++)
            {
                num[i] = new double[3];
                input = Console.ReadLine();
                arrayTemp = input.Split(' ');
                num[i] = arrayTemp.Select(double.Parse).ToArray();
            }

            double a1 = 0;
            double b1 = num[0][0] - a1;
            double a2 = num[1][0] - b1;
            double a3 = num[2][0] - b1;
            double b2 = num[0][1] - a1;
            double b3 = num[0][2] - a1;
            if (num[1][1] == a2 + b2 && num[1][2] == a2 + b3 && num[2][1] == a3 + b2 && num[2][2] == a3 + b3)
            {
                Console.WriteLine("Yes");
                return;
            }

            for (int i = 1; i <= Math.Ceiling(num[0][0] / 2); i++)
            {
                if (num[1][1] == a2 + b2 && num[1][2] == a2 + b3 && num[2][1] == a3 + b2 && num[2][2] == a3 + b3)
                {
                    Console.WriteLine("Yes");
                    return;
                }
                a1 = i;
                b1 = num[0][0] - a1;
                a2 = num[1][0] - b1;
                a3 = num[2][0] - b1;
                b2 = num[0][1] - a1;
                b3 = num[0][2] - a2;
            }
            Console.WriteLine("No");
        }
    }
}