Problem:
Score : 300 points

Problem Statement

We will call a string obtained by arranging the characters contained in a string a in some order, an anagram of a.

For example, greenbin is an anagram of beginner. As seen here, when the same character occurs multiple times, that character must be used that number of times.

Given are N strings s_1, s_2, \ldots, s_N. Each of these strings has a length of 10 and consists of lowercase English characters. Additionally, all of these strings are distinct. Find the number of pairs of integers i, j (1 \leq i < j \leq N) such that s_i is an anagram of s_j.

Constraints

2 \leq N \leq 10^5

s_i is a string of length 10.

Each character in s_i is a lowercase English letter.

s_1, s_2, \ldots, s_N are all distinct.

Input

Input is given from Standard Input in the following format:

N
s_1
s_2
:
s_N

Output

Print the number of pairs of integers i, j (1 \leq i < j \leq N) such that s_i is an anagram of s_j.

Sample Input 1

3
acornistnt
peanutbomb
constraint

Sample Output 1

1

s_1 = acornistnt is an anagram of s_3 = constraint. There are no other pairs i, j such that s_i is an anagram of s_j, so the answer is 1.

Sample Input 2

2
oneplustwo
ninemodsix

Sample Output 2

0

If there is no pair i, j such that s_i is an anagram of s_j, print 0.

Sample Input 3

5
abaaaaaaaa
oneplustwo
aaaaaaaaba
twoplusone
aaaabaaaaa

Sample Output 3

4

Note that the answer may not fit into a 32-bit integer type, though we cannot put such a case here.

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;

namespace Sandbox
{
    internal class ProgramC
    {
        private static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();
            var ss = new string[n];
            var checkStrings = new HashSet<int>();
            var charCounts = new Dictionary<int, Dictionary<int, HashSet<int>>>();
            var charCountList = new int[n, 26];

            for (var i = 0; i < n; i++)
            {
                var s = scanner.GetNext();
                ss[i] = s;

                var charCount = new int[26];

                foreach (var c in s)
                {
                    charCount[c - 'a']++;
                    charCountList[i, c - 'a']++;
                }

                for (var ci = 0; ci < charCount.Length; ci++)
                {
                    var iCount = charCount[ci];
                    if (iCount == 0)
                    {
                        continue;
                    }

                    if (!charCounts.ContainsKey(ci))
                    {
                        charCounts[ci] = new Dictionary<int, HashSet<int>>();
                    }

                    if (!charCounts[ci].ContainsKey(iCount))
                    {
                        charCounts[ci][iCount] = new HashSet<int>();
                    }
                    charCounts[ci][iCount].Add(i);
                }
            }

            var counter = 0L;
            for (var i = 0; i < n; i++)
            {
                if (checkStrings.Contains(i))
                {
                    continue;
                }

                HashSet<int> set = null;

                for (var ci = 0; ci < 26; ci++)
                {
                    var charCount = charCountList[i, ci];
                    if (charCount == 0)
                    {
                        continue;
                    }

                    var tmpSet = charCounts[ci][charCount];
                    if (set == null)
                    {
                        set = tmpSet;
                    }
                    else
                    {
                        var tmp = new HashSet<int>();
                        foreach (var i1 in tmpSet)
                        {
                            if (set.Contains(i1))
                            {
                                tmp.Add(i1);
                            }
                        }
                        set = tmp;
                    }
                }

                if (set.Count == 1)
                {
                    continue;
                }

                foreach (var ii in set)
                {
                    checkStrings.Add(ii);
                }

                counter += nCm(set.Count, 2);
            }

            Console.WriteLine(counter);
        }

        public static long nCm(long n, long m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * nCm(n - 1, m - 1) / m;
        }
        #region String Scanner

        public class Scanner
        {
            private const char Separator = ' ';
            private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
            private int _Pos;
            private string[] _Line = new string[0];

            #region get a element

            public string GetNext()
            {
                // ReSharper disable once InvertIf
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                    this._Pos = 0;
                }

                return this._Line[this._Pos++];
            }

            public int GetNextAsInt()
            {
                return int.Parse(this.GetNext());
            }

            public long GetNextAsLong()
            {
                return long.Parse(this.GetNext());
            }

            public double GetNextAsDouble()
            {
                return double.Parse(this.GetNext());
            }

            #endregion

            #region get array

            public string[] ToArrayFromNextLine()
            {
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                }

                this._Pos = this._Line.Length;
                return this._Line;
            }

            public int[] ToIntArrayFromNextLine()
            {
                return ToIntArray(this.ToArrayFromNextLine());
            }

            public long[] ToLongArrayFromNextLine()
            {
                return ToLongArray(this.ToArrayFromNextLine());
            }

            public double[] ToDoubleArrayFromNextLine()
            {
                return ToDoubleArray(this.ToArrayFromNextLine());
            }

            #endregion

            #region convert array

            private static int[] ToIntArray(string[] array)
            {
                var result = new int[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = int.Parse(array[i]);
                }

                return result;
            }

            private static long[] ToLongArray(string[] array)
            {
                var result = new long[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = long.Parse(array[i]);
                }

                return result;
            }

            private static double[] ToDoubleArray(string[] array)
            {
                var result = new double[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = double.Parse(array[i]);
                }

                return result;
            }

            #endregion
        }

        #endregion
    }
}