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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net.NetworkInformation;
using System.Security.Cryptography;
using System.Text;
using System.Threading;
using Extensions;
using static System.Math;
using static Extensions.MathExtension;
using static Extensions.ConsoleInputExtension;
using static Extensions.ConsoleOutputExtension;

class Solver
{
    public void Solve()
    {
        //Solve Code Here
        int N = Cin;
        var s = new List<string>();
        for (int i = 0; i < N; i++) s.Add(new string(((string) Cin).OrderBy(val => val).ToArray()));
        s.Sort();
        string old = "";
        int count = 1;
        long sum = 0;
        for (int i = 0; i < N; i++)
        {
            if (s[i] == old)
            {
                count++;
            }
            else
            {
                sum += (count * (count - 1)) >> 1;
                count = 1;
                old = s[i];
            }
        }

        sum += (count * (count - 1)) >> 1;

        Coutln(sum);
    }

    //Other Functions Here
}
//Other Classes Here

#if !DEBUG
class EntryPoint
{
    static void Main(string[] args)
    {
        new Solver().Solve();
        Flush();
    }
}
#endif

class PriorityQueue<T>
{
    private readonly List<Tuple<int, T>> _list = new List<Tuple<int, T>>();
    public int Count { get; private set; } = 0;

    public PriorityQueue()
    {
        _list.Add(null);
        _list.Add(null);
        _list.Add(null);
    }

    public void Push(T item, int priority)
    {
        var itemIndex = Count++;
        _list[itemIndex] = Tuple.Create(priority, item);
        while (_list.Count < Count + 2) _list.Add(null);

        int parentIndex;
        while ((parentIndex = GetParentIndex(itemIndex)) != -1 && priority > _list[parentIndex].Item1)
        {
            Swap(itemIndex, parentIndex);
            itemIndex = parentIndex;
        }
    }

    private int GetParentIndex(int index)
    {
        if (index == 0) return -1;
        return ((index + 1) >> 1) - 1;
    }

    private Tuple<int, int> GetChildrenIndex(int index)
    {
        var item2 = (index + 1) << 1;
        var item1 = item2 - 1;
        return item2 >= _list.Count ? null : Tuple.Create(item1, item2);
    }

    public T Pop()
    {
        if (_list.Count <= 0 || _list[0] == null) throw new IndexOutOfRangeException();
        var item = _list[0].Item2;
        _list[0] = null;
        Tuple<int, int> childrenIndex;
        int index = 0;
        while ((childrenIndex = GetChildrenIndex(index)) != null &&
               (_list[childrenIndex.Item1] != null || _list[childrenIndex.Item2] != null))
        {
            if ((_list[childrenIndex.Item1] != null && _list[childrenIndex.Item2] != null &&
                 _list[childrenIndex.Item1].Item1 > _list[childrenIndex.Item2].Item1) ||
                _list[childrenIndex.Item2] == null)
            {
                _list[index] = _list[childrenIndex.Item1];
                _list[childrenIndex.Item1] = null;
                index = childrenIndex.Item1;
            }
            else
            {
                two:
                _list[index] = _list[childrenIndex.Item2];
                _list[childrenIndex.Item2] = null;
                index = childrenIndex.Item2;
            }
        }

        Count--;
        return item;
    }

    public T Peek()
    {
        return _list[0].Item2;
    }

    private void Swap(int index1, int index2)
    {
        var tmp = _list[index1];
        _list[index1] = _list[index2];
        _list[index2] = tmp;
    }
}

struct Rational
{
    private long _numerator;
    private long _denominator;
    public long Numerator => _numerator;
    public long Denominator => _denominator;

    public Rational(long numerator, long denominator)
    {
        var gcd = GCD(numerator, denominator);
        _numerator = numerator / gcd;
        _denominator = denominator / gcd;
    }

    public static Rational operator +(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator + b._numerator * a._denominator,
            a._denominator * b._denominator);
    }

    public static Rational operator -(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator - b._numerator * a._denominator,
            a._denominator * b._denominator);
    }

    public static Rational operator *(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._numerator, a._denominator * b._denominator);
    }

    public static Rational operator /(Rational a, Rational b)
    {
        return new Rational(a._numerator * b._denominator, a._denominator * b._numerator);
    }

    public static explicit operator Rational(int i)
    {
        return new Rational(i, 1);
    }

    public static explicit operator Rational(long l)
    {
        return new Rational(l, 1);
    }

    public static explicit operator Rational(double d)
    {
        long denominator = 1;
        while (d % 1 != 0)
        {
            denominator *= 2;
            d *= 2;
        }

        return new Rational((long) d, denominator);
    }

    public static explicit operator Rational(float f)
    {
        long denominator = 1;
        while (f % 1 != 0)
        {
            denominator *= 2;
            f *= 2;
        }

        return new Rational((long) f, denominator);
    }
}

struct ModInt
{
    public long Value { get; }
    public static long Mod { get; set; } = 1000000000L + 7;

    public ModInt(long l)
    {
        long value = l % Mod;
        while (value < 0) value += Mod;
        Value = value % Mod;
    }

    public static implicit operator long(ModInt m)
    {
        return m.Value;
    }

    public static explicit operator ModInt(long l)
    {
        return new ModInt(l);
    }

    public static ModInt operator +(ModInt a, ModInt b)
    {
        return new ModInt(a.Value + b.Value);
    }

    public static ModInt operator -(ModInt a, ModInt b)
    {
        return new ModInt(a.Value - b.Value);
    }

    public static ModInt operator *(ModInt a, ModInt b)
    {
        return new ModInt(a.Value * b.Value);
    }

    public static ModInt operator /(ModInt a, ModInt b)
    {
        return new ModInt(a * b.Inverse());
    }

    public override string ToString()
    {
        return Value.ToString();
    }
}

static class ModIntMath
{
    public static ModInt Pow(this ModInt a, ModInt b)
    {
        var pow = b.Value;
        var m = a;
        ModInt ans = new ModInt(1);
        while (pow != 0)
        {
            if ((pow & 1) == 1)
            {
                ans *= m;
            }

            pow >>= 1;
            m *= m;
        }

        return ans;
    }

    public static ModInt Inverse(this ModInt m)
    {
        return m.Pow((ModInt) (ModInt.Mod - 2));
    }
}

class UnionFind
{
    private readonly int[] _array;

    public UnionFind(int N)
    {
        _array = new int[N];
        for (int i = 0; i < N; i++)
        {
            _array[i] = i;
        }
    }

    public int GetRootNode(int n)
    {
        if (_array[n] == n) return n;
        return _array[n] = GetRootNode(_array[n]);
    }

    public void UnionGroup(int a, int b)
    {
        var rootA = GetRootNode(a);
        var rootB = GetRootNode(b);
        if (rootA == rootB) return;
        _array[rootA] = rootB;
    }

    public bool IsSameGroup(int a, int b) => GetRootNode(a) == GetRootNode(b);

    public bool IsRoot(int n) => _array[n] == n;
}


namespace Extensions
{
    public class ConsoleInputExtension
    {
        private static readonly ConsoleInputExtension _cin = new ConsoleInputExtension();

        public static ConsoleInputExtension Cin => _cin;

        private static readonly Queue<string> _inputQueue = new Queue<string>();

        private ConsoleInputExtension()
        {
        }

        public static implicit operator string(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return _inputQueue.Dequeue();
        }

        public static implicit operator int(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return int.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator long(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return long.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator float(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return float.Parse(_inputQueue.Dequeue());
        }

        public static implicit operator double(ConsoleInputExtension _)
        {
            if (_inputQueue.Count == 0) Console.ReadLine().Split(' ').ForEach(val => _inputQueue.Enqueue(val));
            return double.Parse(_inputQueue.Dequeue());
        }
    }

    public static class ConsoleOutputExtension
    {
        private static StringBuilder _builder = new StringBuilder();

        public static void Cout(object o)
        {
            _builder.Append(o);
        }

        public static void CoutF(object o)
        {
            _builder.Append(o);
            Flush();
        }

        public static void Coutln(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
        }

        public static void Coutln()
        {
            _builder.Append('\n');
        }

        public static void CoutlnF(object o)
        {
            _builder.Append(o);
            _builder.Append('\n');
            Flush();
        }

        public static void Flush()
        {
            Console.Write(_builder.ToString());
            _builder.Clear();
        }
    }

    public static class MathExtension
    {
        //最小公倍数
        public static int LCM(int num1, int num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        public static long LCM(long num1, long num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        //最大公約数
        public static int GCD(int num1, int num2)
        {
            int a = Math.Max(num1, num2);
            int b = Math.Min(num1, num2);
            int mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        public static long GCD(long num1, long num2)
        {
            long a = Math.Max(num1, num2);
            long b = Math.Min(num1, num2);
            long mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }
    }

    public static class EnumerableExtension
    {
        public delegate void Function<in T>(T val);

        public static void ForEach<T>(this IEnumerable<T> enumerable, Function<T> function)
        {
            foreach (var x in enumerable)
            {
                function(x);
            }
        }
    }
}