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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static Ha2ne2Util.Cin;
using static Ha2ne2Util.Util;
using static System.Console;
using static System.Math;
using System.Collections;
using Pair = System.Tuple<long, long>;
using Ha2ne2Util;

/// <summary>
/// https://atcoder.jp/contests/abc137
/// 2020/02/12 
/// </summary>
namespace ABC137
{
    public class Program
    {
        public static void Main(string[] args)
        {
            // A(); 3m
            // B(); 10m
            C();
            // D();
            // E();
            // F();
        }

        public static void F()
        {

        }

        public static void E()
        {

        }

        public static void D()
        {

        }

        public static void C()
        {
            long N = rl;
            string[] s = new string[N];
            for (int i = 0; i < N; i++)
            {
                s[i] = rs;
            }

            HashMap<string, int> hm = new HashMap<string,int>();
            foreach(var str in s)
            {
                hm[new string(str.OrderBy(c => c).ToArray())]++;
            }

            long ans = 0;
            foreach(var val in hm.Values)
            {
                ans += val * (val - 1) / 2;
            }

            Console.WriteLine(ans);

        }

        public static void B()
        {
            long K = rl;
            long X = rl;

            StringBuilder sb = new StringBuilder();                        
            for (int i = (int)(X-K+1); i <= X+K-1; i++)
            {
                sb.Append(i + " ");
            }

            Console.WriteLine(sb.ToString());
        }

        public static void A()
        {
            long A = rl;
            long B = rl;

            long plus = A + B;
            long minus = A - B;
            long mul = A * B;

            Console.WriteLine(Max(Max(plus, minus), mul));
        }
    }
}

namespace Ha2ne2Util
{
    public static class Cin
    {
        #region public

        public static long rl => ReadLong();
        public static long[] rla => ReadLongArray();
        public static double rd => ReadDouble();
        public static double[] rda => ReadDoubleArray();
        public static string rs => ReadString();

        public static int ReadInt()
        {
            return int.Parse(Next());
        }

        public static long ReadLong()
        {
            return long.Parse(Next());
        }

        public static double ReadDouble()
        {
            return double.Parse(Next());
        }

        public static string ReadString()
        {
            return Next();
        }

        public static int[] ReadIntArray()
        {
            Tokens = null;
            return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        }

        public static long[] ReadLongArray()
        {
            Tokens = null;
            return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        }

        public static double[] ReadDoubleArray()
        {
            Tokens = null;
            return Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
        }

        public static void ReadCols(out long[] a, out long[] b, long N)
        {
            a = new long[N];
            b = new long[N];
            for (int i = 0; i < N; i++)
            {
                a[i] = ReadLong();
                b[i] = ReadLong();
            }
        }

        public static void ReadCols(out long[] a, out long[] b, out long[] c, long N)
        {
            a = new long[N];
            b = new long[N];
            c = new long[N];
            for (int i = 0; i < N; i++)
            {
                a[i] = ReadLong();
                b[i] = ReadLong();
                c[i] = ReadLong();
            }
        }

        public static int[][] ReadIntTable(int n)
        {
            Tokens = null;
            int[][] ret = new int[n][];
            for (int i = 0; i < n; i++)
            {
                ret[i] = ReadIntArray();
            }

            return ret;
        }

        public static long[][] ReadLongTable(long n)
        {
            Tokens = null;
            long[][] ret = new long[n][];
            for (long i = 0; i < n; i++)
            {
                ret[i] = ReadLongArray();
            }

            return ret;
        }

        #endregion

        #region private

        private static string[] Tokens { get; set; }

        private static int Pointer { get; set; }

        public static string Next()
        {
            if (Tokens == null || Tokens.Length <= Pointer)
            {
                Tokens = Console.ReadLine().Split(' ');
                Pointer = 0;
            }

            return Tokens[Pointer++];
        }

        #endregion

    }

    /// <summary>
    /// ユーティリティー
    /// </summary>
    public static class Util
    {
        // 10^17
        public static readonly long INF = (long)1e17;

        // 10^9 + 7
        public readonly static long MOD = (long)1e9 + 7;

        /// <summary>
        /// Console.WriteLineの自動フラッシュをしないようにする
        /// </summary>
        public static void DontAutoFlush()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
        }

        public static void Flush()
        {
            Console.Out.Flush();
        }

        public static IEnumerable<int> Range(int end)
        {
            for (int i = 0; i < end; i++)
            {
                yield return i;
            }
        }

        public static IEnumerable<int> Range(int from, int end)
        {
            for (int i = from; i < end; i++)
            {
                yield return i;
            }
        }

        public static IEnumerable<int> Range(int from, int end, int step)
        {
            for (int i = from; i < end; i += step)
            {
                yield return i;
            }
        }

        /// <summary>
        /// ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] Sort<T>(T[] array)
        {
            Array.Sort<T>(array);
            return array;
        }

        /// <summary>
        /// 降順ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] SortDecend<T>(T[] array)
        {
            Array.Sort<T>(array);
            Array.Reverse(array);
            return array;
        }

        /// <summary>
        /// 引数aと引数bの値を入れ替えます
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="a"></param>
        /// <param name="b"></param>
        public static void Swap<T>(ref T a, ref T b)
        {
            T _a = a;
            a = b;
            b = _a;
        }

        /// <summary>
        /// 先頭と末尾に要素を増やした新しい配列を返します。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] AddHeadAndTail<T>(T[] array)
        {
            int len = array.Length;
            T[] res = new T[len + 2];
            Array.Copy(array, 0, res, 1, len);
            return res;
        }

        /// <summary>
        /// 昇順ソート済みの配列を2分探索します。
        /// 要素が見つからなかった場合はnより大きい数値の中で最小の数値のインデックスを返す。
        /// </summary>
        /// <param name="array"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static int BinarySearch(long[] array, long n)
        {
            int left = 0;
            int right = array.Length - 1;

            while (left <= right)
            {
                int mid = (right - left) / 2 + left;

                if (array[mid] == n)
                {
                    return mid;
                }
                else if (n < array[mid])
                {
                    right = mid - 1;
                }
                else
                {
                    left = mid + 1;
                }
            }

            return left;
        }

        public static int GCD(int a, int b)
        {
            return (b == 0) ? a : GCD(b, a % b);
        }

        /// <summary>
        /// nの約数の配列を返します。
        /// 配列は昇順ソートされています。
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        public static int[] GetDivisor(int n)
        {
            double sqrt = Math.Sqrt(n);

            List<int> divisor = new List<int>();

            for (int i = 1; i <= sqrt; i++)
            {
                if (n % i == 0)
                {
                    divisor.Add(i);
                    int d = n / i;
                    if (d != i)
                    {
                        divisor.Add(d);
                    }
                }
            }

            return Sort(divisor.ToArray());
        }

        public static void Deconstruct<T>(this T[] items, out T t0)
        {
            t0 = items.Length > 0 ? items[0] : default(T);
        }

        public static void Deconstruct<T>(this T[] items, out T t0, out T t1)
        {
            if (items.Length < 2)
                throw new ArgumentException();

            t0 = items[0];
            t1 = items[1];
        }

        public static void Deconstruct<T>(this T[] items, out T t0, out T t1, out T t2)
        {
            if (items.Length < 3)
                throw new ArgumentException();

            t0 = items[0];
            t1 = items[1];
            t2 = items[2];
        }

        public static void Deconstruct<T>(this T[] items, out T t0, out T t1, out T t2, out T t3)
        {
            if (items.Length < 4)
                throw new ArgumentException();

            t0 = items[0];
            t1 = items[1];
            t2 = items[2];
            t3 = items[3];
        }

        public static void ChMax(ref long a, long b)
        {
            if (a < b) a = b;
        }

        public static void ChMin(ref long a, long b)
        {
            if (a > b) a = b;
        }

        public static long ModAdd(long a, long b)
        {
            long res = a + b;
            if (res >= MOD)
                return res % MOD;
            return res;
        }

        public static long ModMul(long a, long b)
        {
            long res = a * b;
            if (res >= MOD)
                return res % MOD;
            return res;
        }

        public static void ChModAdd(ref long a, long b)
        {
            a += b;
            if (a >= MOD)
                a %= MOD;
        }

        public static void ChModMul(ref long a, long b)
        {
            a *= b;
            if (a >= MOD)
                a %= MOD;
        }

        public static T MinBy<T>(this IEnumerable<T> source, Func<T, long> conv)
        {
            T min = source.First();
            long minValue = long.MaxValue;
            foreach (T x in source)
            {
                long n = conv(x);
                if (n < minValue)
                {
                    min = x;
                }
            }

            return min;
        }

        public static T MaxBy<T>(this IEnumerable<T> source, Func<T, long> conv)
        {
            T min = source.First();
            long maxValue = long.MinValue;
            foreach (T x in source)
            {
                long n = conv(x);
                if (maxValue < n)
                {
                    min = x;
                }
            }

            return min;
        }

        public static void FillArray<T>(T[] array, T value)
        {
            int max = array.Length;
            for (int i = 0; i < max; i++)
            {
                array[i] = value;
            }
        }

        public static void FillArray<T>(T[,] array, T value)
        {
            int max0 = array.GetLength(0);
            int max1 = array.GetLength(1);

            for (int i = 0; i < max0; i++)
            {
                for (int j = 0; j < max1; j++)
                {
                    array[i, j] = value;
                }
            }
        }

        public static void FillArray<T>(T[,,] array, T value)
        {
            int max0 = array.GetLength(0);
            int max1 = array.GetLength(1);
            int max2 = array.GetLength(2);

            for (int i = 0; i < max0; i++)
            {
                for (int j = 0; j < max1; j++)
                {
                    for (int k = 0; k < max2; k++)
                    {
                        array[i, j, k] = value;
                    }
                }
            }
        }

        /// <summary>
        /// 累積和を求めて返します。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static long[] Accumulate(long[] array)
        {
            long[] acc = new long[array.Length + 1];
            for (int i = 0; i < array.Length; i++)
            {
                acc[i + 1] = acc[i] + array[i];
            }
            return acc;
        }
        public static double[] Accumulate(double[] array)
        {
            double[] acc = new double[array.Length + 1];
            for (int i = 0; i < array.Length; i++)
            {
                acc[i + 1] = acc[i] + array[i];
            }
            return acc;
        }

        /// <summary>
        /// めぐる式二分探索
        /// okにはpredを満たすindexを、ngにはpredを満たさないindexを指定します。
        /// 引数がng＜okの場合、最小のokとなるindexをokに代入します。(lower_bound）
        /// 引数がok＜ngの場合、最大のokとなるindexをokに代入します。(upper_bound）
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <param name="okIndex"></param>
        /// <param name="ngIndex"></param>
        /// <param name="pred"></param>
        public static void MeguruBinarySearch<T>(
            T[] array,
            ref long okIndex,
            ref long ngIndex,
            Predicate<T> pred)
        {
            while (Math.Abs(okIndex - ngIndex) > 1)
            {
                long mid = (okIndex + ngIndex) / 2;
                if (pred(array[mid]))
                {
                    okIndex = mid;
                }
                else
                {
                    ngIndex = mid;
                }
            }
        }
    }

    public class HashMap<K, V> : Dictionary<K, V>
    {
        private V DefaltValue;
        public HashMap() { }
        public HashMap(V defaultValue)
        {
            DefaltValue = defaultValue;
        }
        new public V this[K i]
        {
            get
            {
                V v;
                return TryGetValue(i, out v) ? v : base[i] = DefaltValue;
            }
            set { base[i] = value; }
        }
    }

    /// <summary>
    /// UnionFindTree
    /// </summary>
    public class UnionFindTree
    {
        public int[] Node;

        public UnionFindTree(int N)
        {
            Node = new int[N];
            for (int i = 0; i < N; i++)
            {
                Node[i] = -1;
            }
        }

        public bool IsSameGroup(int x, int y)
        {
            return GetRoot(x) == GetRoot(y);
        }

        public bool Merge(int x, int y)
        {
            int xr = GetRoot(x);
            int yr = GetRoot(y);

            if (xr == yr)
                return false;

            // xが、大きなグループを示すようにSwapする（値が小さい方が大きなグループ）
            if (Node[xr] > Node[yr])
                Swap(ref xr, ref yr);

            // グループの数を合算する
            Node[xr] += Node[yr];

            // 根を張り替える
            Node[yr] = xr;
            return true;
        }

        public int Size(int x)
        {
            return -Node[GetRoot(x)];
        }

        public int GetRoot(int n)
        {
            if (Node[n] < 0)
            {
                return n;
            }
            else
            {
                // 根を張りなおす。
                Node[n] = GetRoot(Node[n]);
                return Node[n];
            }
        }
    }

    /// <summary>
    /// PriorityQueue
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class PriorityQueue<T>
    {
        private Comparison<T> _comparison = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        public PriorityQueue(int maxSize, Comparison<T> comparison)
        {
            _heap = new T[maxSize];
            _comparison = comparison;
        }

        private int Compare(T x, T y)
        {
            return _comparison(x, y);
            //if (_comparison != null) return _comparison(x, y);
            //return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }
}