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: Accepted)

using System;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.IO;
using System.Text;

public class Solver
{
    public void Solve()
    {
        int n = ri;
        Dictionary<string, int> s = new Dictionary<string, int>();
        string t = "";
        char[] c = new char[10];
        long p = 0;
        for(int i = 0; i < n; i++)
        {
            t = rs;
            for(int j = 0; j < 10; j++)
            {
                c[j] = t[j];
            }
            Array.Sort(c);
            t = string.Join("", c);
            if (s.Keys.Contains(t))
            {
                p += s[t];
                s[t]++;
            }
            else
            {
                s.Add(t, 1);
            }
        }
        Write(p);
    }

    int ri { get { return sc.Integer(); } }
    long rl { get { return sc.Long(); } }
    double rd { get { return sc.Double(); } }
    string rs { get { return sc.Scan(); } }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    
    private const long mod = 1000000007;
    long Reverse(long n) { return Pow(n, mod - 2); }
    int Sign(int n) { return n == 0 ? 0 : n > 0 ? 1 : -1; }
    int Abs(int n) { return (n > 0) ? n : -n; }
    int Gcd(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    int Gcd(int a, int b) { return (a == 0) ? b : Gcd(b % a, a); }
    int Lcm(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    int Lcm(int a, int b) { return a * b / Gcd(a, b); }
    int Max(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = (p > n[i]) ? p : n[i]; } return p; }
    int Min(params int[] n) { int p = n[0]; for (int i = 1; i < n.Length; i++) { p = (p < n[i]) ? p : n[i]; } return p; }
    long Mul(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p * n[i]) % mod; } return p; }
    long Pow(long n, long p) { long t = n, q = 1; while (p > 0) { if (p % 2 == 1) { q = (q * t) % mod; } t = (t * t) % mod; p >>= 1; } return q; }
    long PowUpper(long n, long b) { long p = 1; while (p <= n) { p *= b; } return p; }
    long Sign(long n) { return n == 0 ? 0 : n > 0 ? 1 : -1; }
    long Abs(long n) { return (n > 0) ? n : -n; }
    long Gcd(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = Gcd(p, n[i]); } return p; }
    long Gcd(long a, long b) { return (a == 0) ? b : Gcd(b % a, a); }
    long Lcm(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = Lcm(p, n[i]); } return p; }
    long Lcm(long a, long b) { return a * b / Gcd(a, b); }
    long Max(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p > n[i]) ? p : n[i]; } return p; }
    long Min(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p < n[i]) ? p : n[i]; } return p; }
    void Write<T>(T t) { Console.WriteLine(t.ToString()); }
    void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
}

static class Program
{
    static public void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}

public class StreamScanner
{
    public StreamScanner(Stream stream) { str = stream; }
    private readonly Stream str;
    private readonly byte[] buf = new byte[1024];
    private int len, ptr;
    public bool isEof = false;
    public bool IsEndOfStream { get { return isEof; } }
    private byte read()
    {
        if (isEof) throw new EndOfStreamException();
        if (ptr >= len)
        {
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) <= 0)
            {
                isEof = true;
                return 0;
            }
        }
        return buf[ptr++];
    }
    public char Char()
    {
        byte b = 0;
        do b = read();
        while (b < 33 || 126 < b);
        return (char)b;
    }
    public string Scan()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
            sb.Append(b);
        return sb.ToString();
    }
    public long Long()
    {
        long ret = 0; byte b = 0; var ng = false;
        do b = read();
        while (b != '-' && (b < '0' || '9' < b));
        if (b == '-') { ng = true; b = read(); }
        for (; true; b = read())
        {
            if (b < '0' || '9' < b)
                return ng ? -ret : ret;
            else ret = ret * 10 + b - '0';
        }
    }
    public int Integer() { return (int)Long(); }
    public double Double() { return double.Parse(Scan()); }
}