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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var t = new int[3][];
        for (int i = 0; i < 3; i++) {
            t[i] = ToIntArray(input.ReadLine(), 3);
        }

        for(int a1=0; a1<=100; a1++) {
            var b1 = t[0][0] - a1;
            var b2 = t[0][1] - a1;
            var b3 = t[0][2] - a1;
            var a2 = t[1][0] - b1;
            var a3 = t[2][0] - b1;

            bool ok = true;
            ok &= t[0][0] == a1 + b1;
            ok &= t[0][1] == a1 + b2;
            ok &= t[0][2] == a1 + b3;
            ok &= t[1][0] == a2 + b1;
            ok &= t[1][1] == a2 + b2;
            ok &= t[1][2] == a2 + b3;
            ok &= t[2][0] == a3 + b1;
            ok &= t[2][1] == a3 + b2;
            ok &= t[2][2] == a3 + b3;
            if (ok) return Yes;
        }

        return No;
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }
}