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)

/*
csc -debug C.cs && mono --debug C.exe <<< "3
acornistnt
peanutbomb
constraint"
*/

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading;
using System.Reflection;

public class HelloWorld {
    public static void SolveCodeForces() {
        var N = cin.NextInt();
        var C = new Counter<string>();
        for (var i = 0; i < N; i++) {
            var S = Console.ReadLine().ToCharArray();
            Array.Sort(S, 0, S.Length);
            C[new string(S)]++;
        }

        var ans = 0L;

        foreach (var kvp in C.Dict) {
            var cnt = (long)kvp.Value;
            ans += cnt * (cnt - 1) / 2;
// System.Console.WriteLine(new {key = kvp.Key, value = kvp.Value});
        }

        System.Console.WriteLine(ans);
    }

    static Scanner cin = new Scanner();
    static StringBuilder cout = new StringBuilder();

    static public void Main () {
        SolveCodeForces();
        // IncreaseStack(SolveCodeForces);
        // System.Console.Write(cout.ToString());
    }

    public static void IncreaseStack(ThreadStart action, int stackSize = 128000000)
    {
        var thread = new Thread(action, stackSize);
        thread.Start();
        thread.Join();
    }
}

public class Counter<T> {
    public Dictionary<T, int> Dict;
    public Counter() { Dict = new Dictionary<T, int>(); }
    public Counter(IEnumerable<T> keys) { Dict = new Dictionary<T, int>(); foreach (var k in keys) Add(k, 1); }
    public int this[T key] {
        get { int res; return Dict.TryGetValue(key, out res) ? res : 0; }
        set { Dict[key] = value; }
    }
    public void Add(T key, int add) { int res; if (Dict.TryGetValue(key, out res)) Dict[key] = res + add; else Dict[key] = add; }
}

public static class Helpers {
    public static string Join<T>(this IEnumerable<T> arr, string sep = " ") {
        return string.Join(sep, arr);
    }

    public static void Swap<T>(ref T a, ref T b) {
        var tmp = a;
        a = b;
        b = tmp;
    }

    public static T[] CreateArray<T>(int length, Func<int, T> itemCreate) {
        var result = new T[length];
        for (var i = 0; i < result.Length; i++)
            result[i] = itemCreate(i);
        return result;
    }
}

public class Scanner
{
    private string[] line = new string[0];
    private int index = 0;

    public string Next() {
        if (line.Length <= index) {
            line = Console.ReadLine().Split(' ');
            index = 0;
        }
        var res = line[index];
        index++;
        return res;
    }

    public int NextInt() {
        return int.Parse(Next());
    }

    public long NextLong() {
        return long.Parse(Next());
    }

    public ulong NextUlong() {
        return ulong.Parse(Next());
    }

    public string[] Array() {
        line = Console.ReadLine().Split(' ');
        index = line.Length;
        return line;
    }

    public int[] IntArray(int emptyPrefixLen = 0) {
        var array = Array();
        var result = new int[emptyPrefixLen + array.Length];
        for (int i = 0; i < array.Length; i++)
            result[emptyPrefixLen + i] = int.Parse(array[i]);
        return result;
    }

    public long[] LongArray() {
        var array = Array();
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
            result[i] = long.Parse(array[i]);
        return result;
    }

    public ulong[] UlongArray() {
        var array = Array();
        var result = new ulong[array.Length];
        for (int i = 0; i < array.Length; i++)
            result[i] = ulong.Parse(array[i]);
        return result;
    }
}