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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.ExceptionServices;
using System.Security.Authentication.ExtendedProtection;
using System.Text;

namespace cswork
{
    class Program
    {
        class Scanner
        {
            string[] s;
            int i;

            char[] cs = new char[] { ' ' };

            public Scanner()
            {
                s = new string[0];
                i = 0;
            }

            public string next()
            {
                if (i < s.Length) return s[i++];
                string st = Console.ReadLine();
                while (st == "") st = Console.ReadLine();

                s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                i = 0;
                return next();
            }

            public int nextInt()
            {
                return int.Parse(next());
            }

            public long nextLong()
            {
                return long.Parse(next());
            }

            public double nextDouble()
            {
                return double.Parse(next());
            }
        }

        public Program() { }

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

        Scanner cin = new Scanner();
        const int MAXIN = 1024;
        bool[] used = new bool[MAXIN];
        int[] perm = new int[MAXIN];

        List<int[]> permList = new List<int[]>();

        public void Permutation(int pos, int n, int length)
        {
            if (pos == n)
            {
                permList.Add((int[])perm.Clone());
            }

            for (int i = 0; i < n; i++)
            {
                if (!used[i])
                {
                    perm[pos] = i;
                    used[i] = true;
                    Permutation(pos + 1, n, length);
                    used[i] = false;
                }
            }
        }

        public static List<long> GeneratePrime(long max)
        {
            long prime;
            double sqrtMax = Math.Sqrt(max);
            var primeList = new List<long>();

            List<long> searchList = new List<long>();
            for (long i = 2; i <= max - 1; i++)
            {
                searchList.Add(i);
            }

            do
            {
                prime = searchList.First();
                primeList.Add(prime);
                searchList.RemoveAll(n => n % prime == 0);
            } while (prime < sqrtMax);

            primeList.AddRange(searchList);

            return primeList;
        }

        // 最小公倍数
        public static long Lcm(long a, long b)
        {
            return a * b / Gcd(a, b);
        }

        // ユークリッドの互除法 
        public static long Gcd(long a, long b)
        {
            if (a < b)
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }

        public static readonly string Yes = "Yes";
        public static readonly string YES = "YES";
        public static readonly string No = "No";
        public static readonly string NO = "NO";
        public static readonly string OK = "OK";
        public static readonly string NG = "NG";

        void Omame()
        {
            int[,] map = new int[4, 4];
            for (int i = 1; i <= 3; i++)
            {
                for (int j = 1; j <= 3; j++)
                {
                    map[i, j] = cin.nextInt();
                }
            }

            bool flag = false;
            for (int i = 1; i <= 100; i++)
            {
                for (int j = 1; j <= 100; j++)
                {
                    for (int k = 1; k <= 100; k++)
                    {
                        flag = true;
                        int a1 = i;
                        int a2 = j;
                        int a3 = k;
                        int b1 = map[1, 1] - i;
                        int b2 = map[2, 2] - j;
                        int b3 = map[3, 3] - k;

                        if (a1 + b2 != map[1, 2])
                        {
                            flag = false;
                        }
                        if (a1 + b3 != map[1, 3])
                        {
                            flag = false;
                        }
                        if (a2 + b1 != map[2, 1])
                        {
                            flag = false;
                        }
                        if (a2 + b3 != map[2, 3])
                        {
                            flag = false;
                        }
                        if (a3 + b1 != map[3, 1])
                        {
                            flag = false;
                        }
                        if (a3 + b2 != map[3, 2])
                        {
                            flag = false;
                        }

                        if (flag) break;
                    }
                    if (flag) break;
                }
                if (flag) break;
            }

            if (flag)
            {
                Console.WriteLine(Yes);
            }
            else
            {
                Console.WriteLine(No);
            }
        }
    }
}