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 Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;
        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }
            var res = line[index];
            index++;
            return res;
        }
        public int NextInt()
        {
            return int.Parse(Next());
        }
        public long NextLong()
        {
            return long.Parse(Next());
        }
        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }
        public int[] IntArray()
        {
            return Array().Select(int.Parse).ToArray();
        }
        public long[] LongArray()
        {
            return Array().Select(long.Parse).ToArray();
        }
    }

    class Program
    {
        private int[][] c;
        private void Scan()
        {
            var sc = new Scanner();
            c = new int[3][];
            for (int i = 0; i < 3; i++)
            {
                c[i] = sc.IntArray();
            }
        }

        private bool C(int a1)
        {
            int[] a = new int[3];
            int[] b = new int[3];
            a[0] = a1;

            b[0] = c[0][0] - a[0];
            b[1] = c[0][1] - a[0];
            b[2] = c[0][2] - a[0];
            a[1] = c[1][0] - b[0];
            a[2] = c[2][0] - b[0];
            for (int i = 0; i < 3; i++)
            {
                for (int j = 0; j < 3; j++)
                {
                    if(c[i][j]!=a[i]+b[j])
                    {
                        return false;
                    }
                }
            }
            return true;
        }

        public void Solve()
        {
            Scan();
            for(int i=-1000000;i<=1000000;i++)
            {
                if(C(i))
                {
                    Console.WriteLine("Yes");
                    return;
                }

            }
            Console.WriteLine("No");
        }

        static void Main(string[] args)
        {
            new Program().Solve();
        }
    }
}