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;
using System.IO;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {

            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }


        public static long GCM(long x, long y)
        {
            var s = x;
            var t = y;
            if (x < y) GCM(y, x);
            while (y != 0)
            {
                var z = x % y;
                x = y;
                y = z;
            }
            return s / x * t;
        }



        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            var c = new long[3][];
            for (int i = 0; i < 3; i++)
            {
                c[i] = Reads();
               
            }
            bool ans = true;
            for (int i = 0; i < 2; i++)
            {
                bool f1 = c[0][i] - c[0][i + 1] == c[1][i] - c[1][i + 1];
                bool f2 = c[0][i] - c[0][i + 1] == c[2][i] - c[2][i + 1];
                if (!f1 || !f2) ans = false;
            }
            for (int i = 0; i < 2; i++)
            {
                bool f1 = c[i][0] - c[i + 1][0] == c[i][1] - c[i + 1][1];
                bool f2 = c[i][0] - c[i + 1][0] == c[i][2] - c[i + 1][2];
                if (!f1 || !f2) ans = false;
            }
            if (ans) Console.WriteLine("Yes");
            else Console.WriteLine("No");



            Console.Out.Flush();
        }
    }
}