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 static Atcoder;
using System.Threading.Tasks;
using System.ComponentModel;

public class Hello
{

    public static void Main()
    {
        int[] c1 = SpRead(' ').Select(_ => int.Parse(_)).ToArray();
        int[] c2 = SpRead(' ').Select(_ => int.Parse(_)).ToArray();
        int[] c3 = SpRead(' ').Select(_ => int.Parse(_)).ToArray();
        int a0, a1, a2;
        a0 = c1.Min();
        a1 = c2.Min();
        a2 = c3.Min();

        int[] cx1 = new int[3]; Array.Copy(c1, cx1, 3);
        int[] cx2 = new int[3]; Array.Copy(c2, cx2, 3);
        int[] cx3 = new int[3]; Array.Copy(c3, cx3, 3);
        for (int i = 0; i < 3; i++) { cx1[i] -= a0; cx2[i] -= a1; cx3[i] -= a2; }

        int b0, b1, b2;
        b0 = Math.Min(Math.Min(cx1[0], cx2[0]), cx3[0]);
        b1 = Math.Min(Math.Min(cx1[1], cx2[1]), cx3[1]);
        b2 = Math.Min(Math.Min(cx1[2], cx2[2]), cx3[2]);

        bool ans = true;
        if (a0 + b0 != c1[0]) ans = false;
        else if (a0 + b1 != c1[1]) ans = false;
        else if (a0 + b2 != c1[2]) ans = false;
        else if (a1 + b0 != c2[0]) ans = false;
        else if (a1 + b1 != c2[1]) ans = false;
        else if (a1 + b2 != c2[2]) ans = false;
        else if (a2 + b0 != c3[0]) ans = false;
        else if (a2 + b1 != c3[1]) ans = false;
        else if (a2 + b2 != c3[2]) ans = false;

        Console.WriteLine((ans ? "Yes" : "No"));
    }

}


public class Atcoder
{
    static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
    public static int LCM(int a, int b)
    {
        int c = a * b;
        if (a < b) Swap(ref a, ref b);
        int d = a % b;
        while (d != 0)
        {
            a = b;
            b = d;
            d = a % b;
        }
        return c / b;
    }
    public static string strReverce(string s)
    {
        return new string(s.Reverse().ToArray());
    }
    public static int intRead()
    {
        return int.Parse(Console.ReadLine());
    }
    public static bool IsPrime(int n)
    {
        if (n < 2) return false;
        if (n == 2) return true;
        if (n % 2 == 0) return false;

        //double sqrtNum = Math.Sqrt(n);
        for (int i = 3; i < n; i += 2)
        {
            if (n % i == 0) return false;
        }
        return true;
    }
    public static string[] SpRead(char c)
    {
        return Console.ReadLine().Split(c);
    }
}