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.Globalization;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    public class Prog
    {
        const int MOD = 1000000007;
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            new Prog().Solve(new ConsoleInput(Console.In, ' '));
            Console.Out.Flush();
        }

        public void Solve(ConsoleInput cin)
        {
            var n = cin.ReadInt;
            var s = cin.ReadStrArray(n);

            var sorted_s = new List<string>();

            foreach (var c in s)
            {
                sorted_s.Add(String.Concat(c.OrderBy(x => x)));
            }

            Array.Sort(sorted_s.ToArray(), StringComparer.InvariantCulture);

            var sameDic = new Dictionary<string, int>();
            foreach (var item in sorted_s)
            {
                if (sameDic.ContainsKey(item))
                {
                    sameDic[item]++;
                }
                else
                {
                    sameDic.Add(item, 1);
                }
            }

            var ans = 0L;
            foreach (var item in sameDic.Values)
            {
                if (item > 1)
                {
                    ans += combination(item);
                }
            }

            Console.WriteLine(ans);
        }
        private long combination(long n)
        {
            var comb = 0L;
            for (int i = 0; i < n; i++)
            {
                var cnt = 0L;
                for (int j = i + 1; j < n; j++)
                {
                    cnt++;
                }
                comb += cnt;
            }
            return comb;
        }

        class Modulo
        {
            private const int M = 1000000007;
            private readonly int[] m_facs;
            public int Mul(int a, int b)
            {
                return (int)(Math.BigMul(a, b) % M);
            }
            public Modulo(int n)
            {
                m_facs = new int[n + 1];
                m_facs[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    m_facs[i] = Mul(m_facs[i - 1], i);
                }
            }
            public int Fac(int n)
            {
                return m_facs[n];
            }
            public int Pow(int a, int m)
            {
                switch (m)
                {
                    case 0:
                        return 1;
                    case 1:
                        return a;
                    default:
                        int p1 = Pow(a, m / 2);
                        int p2 = Mul(p1, p1);
                        return ((m % 2) == 0) ? p2 : Mul(p2, a);
                }
            }
            public int Div(int a, int b)
            {
                return Mul(a, Pow(b, M - 2));
            }
            public int Ncr(int n, int r)
            {
                if (n < r) { return 0; }
                if (n == r) { return 1; }
                int res = Fac(n);
                res = Div(res, Fac(r));
                res = Div(res, Fac(n - r));
                return res;
            }
        }
    }
    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        public void ReadIntArrays(long N, out int[] A, out int[] B) { A = new int[N]; B = new int[N]; for (long i = 0; i < N; ++i) { A[i] = ReadInt; B[i] = ReadInt; } }
    }
}