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;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Gcd(int a, int b)
        {
            if (a < b) { return Gcd(b, a); }
            return (b == 0) ? a : Gcd(b, a % b);
        }
        static int Gcd(int a, int b, int c)
        {
            return Gcd(Gcd(a, b), c);
        }
        static bool Solve(int[][] C)
        {
            if (C[0][1] - C[0][0] != C[1][1] - C[1][0]) { return false; }
            if (C[1][1] - C[1][0] != C[2][1] - C[2][0]) { return false; }
            if (C[0][2] - C[0][1] != C[1][2] - C[1][1]) { return false; }
            if (C[1][2] - C[1][1] != C[2][2] - C[2][1]) { return false; }
            if (C[1][0] - C[0][0] != C[1][1] - C[0][1]) { return false; }
            if (C[1][1] - C[0][1] != C[1][2] - C[0][2]) { return false; }
            if (C[2][0] - C[1][0] != C[2][1] - C[1][1]) { return false; }
            if (C[2][1] - C[1][1] != C[2][2] - C[1][2]) { return false; }
            return true;
        }
        static void Main(string[] args)
        {
            int[][] C = new int[3][];
            for (int i = 0; i < 3; ++i) { C[i] = ReadInts(); }
            Console.WriteLine(Solve(C) ? "Yes" : "No");
        }
    }
}