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 abc088_c
{
    class Program
    {
        static void Main(string[] args)
        {
            var m = new List<List<int>>();
            int a = 0;
            for(int i = 1; i <= 3;i++) 
            {
                var l = GetIntList();
                m.Add(l);
                a += l.Sum();
            }

            if (a % 3 != 0) Console.WriteLine("No");
            else
            {
                var r = a / 3; // a1-b3の和
                var p = Permutation.Enumerate<int>(new List<int> { 0, 1, 2 }, 3, false).ToList();
                var b = true;
                for (int i = 0; i < p.Count(); i++)
                {

                    if (m[0][p[i][0]] + m[1][p[i][1]] + m[2][p[i][2]] != r)
                    {
                        b = false;
                        break;
                    }
                }
                Console.WriteLine(b ? "Yes" : "No");
            }
        }

        public static string GetStr() => Console.ReadLine();
        public static int GetInt() => int.Parse(Console.ReadLine());
        public static long GetLong() => long.Parse(Console.ReadLine());
        public static double GetDouble() => double.Parse(Console.ReadLine());
        public static decimal GetDecimal() => decimal.Parse(Console.ReadLine());

        public static List<string> GetStrList() => Console.ReadLine().Split(' ').ToList();
        public static List<int> GetIntList() => Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToList();
        public static List<long> GetLongList() => Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
        public static List<double> GetDoubleList() => Console.ReadLine().Split(' ').Select(x => double.Parse(x)).ToList();
        public static List<decimal> GetDecimalList() => Console.ReadLine().Split(' ').Select(x => decimal.Parse(x)).ToList();

        /// <summary>
        /// 順列生成クラス
        /// </summary>
        public static class Permutation
        {
            /// <summary>
            /// 順列生成
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="items">選択対象</param>
            /// <param name="k">選択数</param>
            /// <param name="withRepetition">重複を許すかフラグ</param>
            /// <returns></returns>
            public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
            {
                if (k == 1)
                {
                    foreach (var item in items)
                    {
                        yield return new T[] { item };
                    }
                    yield break;
                }
                foreach (var item in items)
                {
                    var leftside = new T[] { item };
                    var unused = withRepetition ? items : items.Except(leftside);
                    foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                    {
                        yield return leftside.Concat(rightside).ToArray();
                    }
                }
            }

            internal static IEnumerable<object[]> Enumerate(string v1, int v2)
            {
                throw new NotImplementedException();
            }
        }

    }
}