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.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
#if !DEBUG
    using System.IO;
#endif


public class Program {
    public static void Main() {
        #region SetAutoFlushIsFalse
#if !DEBUG
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
#endif
        #endregion

        var n = ReadLib.ReadAsInt();
        var words = ReadLib
            .ReadNTimesAsCharArray(n)
            .Select(a => new string(a.OrderBy(c => c).ToArray()));

        var scoreDic = MyMethod
            .CountUp(words)
            .Where(kv => kv.Value >= 2);

        long score = 0;
        foreach (var item in scoreDic) {
            var s = item.Value;
            score += Math.BigMul(s, s - 1) / 2;
        }


        Console.WriteLine(score);
        #region Flush
#if !DEBUG
        Console.Out.Flush();
        sw.Close();
#endif
        #endregion
    }
}


static class Calculation {
}


/// <summary>UnionFind木</summary>
public class UnionFind {
    Dictionary<int, int> nodeToRoot;
    Dictionary<int, int> rank; // その根が配下に何個nodeがぶら下がっているか

    public UnionFind(int n, int startAt = 0) {
        nodeToRoot = Enumerable.Range(startAt, n).ToDictionary(i => i, i => i);    // n個根を作る
        rank = Enumerable.Range(startAt, n).ToDictionary(i => i, i => 0);
    }

    /// <summary>根を得る</summary>
    public int GetRoot(int x) {
        if (nodeToRoot[x] == x) { // 渡されたノードが根
            return x;
        }
        nodeToRoot[x] = GetRoot(nodeToRoot[x]);  // parentの根を得てset。調べるたびに最適化。

        return nodeToRoot[x];
    }

    /// <summary>xとyの木を併合 => 根を同一にする</summary>
   　public void Unite(int x, int y) {
        var rootX = GetRoot(x);
        var rootY = GetRoot(y);

        if (rootX == rootY) {
            return; // pass
        }

        if (rank[rootX] < rank[rootY]) {    // yをxへ併合
            nodeToRoot[rootX] = nodeToRoot[rootY];
        } else {
            nodeToRoot[rootX] = nodeToRoot[rootY];

            if (rank[rootX] == rank[rootY]) {
                rank[rootX]++;  // yの下に配下が1つ追加される。
            }
        }
    }

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

/// <summary>根付き木</summary>
public class RootedTree {
    public int Id { get; }
    public int Parent { get; }
    public int Depth { get; set; }
    int[] Childs { get; }

    public RootedTree(int id, int parent, int[] childs) {
        this.Id = id;
        this.Parent = parent;
        this.Childs = childs;
    }
}



static class Quick {

    internal static void Calculate(int[] ts) {
        QuickSort(ts, 0, ts.Count() - 1);
    }

    private static void QuickSort(int[] ts, int p, int r) {
        if (p < r) {
            var q = Partition(ts, p, r);
            QuickSort(ts, p, q - 1);
            QuickSort(ts, q + 1, r);
        }
    }

    public static int Partition(int[] sArr, int p, int r) {
        var x = sArr[r];
        var i = p - 1;
        for (int j = p; j < r; j++) {
            if (sArr[j] <= x) {
                i++;
                sArr.Swap(i, j);
            }
        }
        sArr.Swap(i + 1, r);
        return i + 1;
    }

}

static class ReadLib {
    public static long ReadAsLong() {
        return long.Parse(Console.ReadLine());
    }

    public static int ReadAsInt() {
        return int.Parse(Console.ReadLine());
    }

    public static int[] ReadAsIntArray(int step = 0) {
        return Console.ReadLine().Split(' ').Select(s => int.Parse(s) + step).ToArray();
    }

    public static long[] ReadAsLongArray(int step = 0) {
        return Console.ReadLine().Split(' ').Select(s => long.Parse(s) + step).ToArray();
    }

    public static ulong[] ReadAsULongArray() {
        return Console.ReadLine().Split(' ').Select(s => ulong.Parse(s)).ToArray();
    }

    public static string[] ReadAsStringArray() {
        return Console.ReadLine().Split(' ');
    }

    public static int[] ReadNTimesAsInt(int n, int step = 0) {
        return Enumerable.Range(1, n).Select(s => int.Parse(Console.ReadLine()) + step).ToArray();
    }

    public static char[][] ReadNTimesAsCharArray(int n) {
        return Enumerable.Range(1, n).Select(i => Console.ReadLine().ToArray()).ToArray();
    }

    public static long[] ReadNTimesAsLong(int n, int step = 0) {
        return Enumerable.Range(1, n).Select(s => long.Parse(Console.ReadLine()) + step).ToArray();
    }

    public static int[][] ReadNTimesAsIntArray(int n, int step = 0) {
        return Enumerable.Range(1, n).Select(s => ReadAsIntArray(step)).ToArray();
    }

    public static string[] ReadNTimesAsString(int n) {
        return Enumerable.Range(1, n).Select(s => Console.ReadLine()).ToArray();
    }

}

static class WriteLib {
    public static void Write<T>(IEnumerable<T> ts) {
        ts.ToList().ForEach(s => Console.WriteLine(s));
    }
}

static class MyMath {
    /// <summary>階乗</summary>
    public static long Factorial(int n) {
        if (n == 0) {
            return 1;
        }

        return Permutation(n, 0);
    }

    public static long Permutation(int n, int k) {
        return Enumerable.Range(0, n - k).Select(i => n - i).Aggregate(1, (b, i) => b * i);
    }

    #region FullPower
    /// <summary>総乗、π</summary>
    public static long FullPower(IEnumerable<long> vs) {
        return vs.Aggregate(1L, (a, b) => a * b);
    }

    public static long FullPower(IEnumerable<int> vs) {
        return vs.Aggregate(1L, (a, b) => a * b);
    }
    #endregion

    /// <summary>最大公約数</summary>
    public static long Gcd(long item1, long item2) {
        var a = Math.Max(item1, item2);
        var b = Math.Min(item1, item2);

        while (true) {
            long mod;
            Math.DivRem(a, b, out mod);
            if (mod == 0) {
                break;
            }

            a = b;
            b = mod;
        }
        return b;
    }

    /// <summary>約分。最大公約数で割ったものを返す。</summary>
    public static Tuple<long, long> DeviedByGcd(long item1, long item2) {
        var gcd = Gcd(item1, item2);
        return new Tuple<long, long>(item1 / gcd, item2 / gcd);
    }

    public static long Lcm(int item1, int item2) {
        return Math.BigMul(item1, item2) / Gcd(item1, item2);
    }

    public static ModCombination ModCombination(int maxN, int mod = 1000000007) {
        return new ModCombination(maxN, mod);
    }

    /// <summary>a^n mod</summary>
    public static int ModPow(long a, long n, int mod = 1000000007) {
        long res = 1;
        long pow = a;

        while (n > 0) {
            if ((n & 1) == 1) {
                res = (pow * res) % mod;    // resにaをかける
            }

            pow = (pow * pow) % mod;    // 次のaはa^2
            n >>= 1;
        }

        return (int)res;
    }
}

static class MyMethod {
    /// <summary>数え上げて、key, 出現回数に変換</summary>
    public static Dictionary<T, int> CountUp<T>(IEnumerable<T> str) {
        return
            str
            .GroupBy(c => c)
            .Select(g => new KeyValuePair<T, int>(g.Key, g.Count()))
            .ToDictionary(e => e.Key, e => e.Value);
    }

    /// <summary>計数ソート</summary>
    public static int[] CountingSort(int[] aArr, int k) {
        int[] b, c;
        var n = aArr.Length;
        b = new int[n];
        c = Enumerable.Repeat(0, k + 1).ToArray();


        for (int i = 0; i < n; i++) {
            c[aArr[i]]++;
        }

        for (int i = 1; i <= k; i++) {
            c[i] += c[i - 1];
        }

        for (int i = n - 1; i >= 0; i--) {
            b[c[aArr[i]] - 1] = aArr[i];
            c[aArr[i]]--;
        }

        return b;
    }
}

/// <summary>無向グラフ</summary>
class UndirectedGraph {
    public Dictionary<int, List<int>> Graph { get; }

    /// <param name="graphArr">point1 to point2</param>
    /// <param name="n">グラフの全要素数</param>
    public UndirectedGraph(int[][] graphArr, int n) {
        Graph = new Dictionary<int, List<int>>();

        for (int i = 1; i <= n; i++) {
            Graph.Add(i, new List<int>());
        }

        foreach (var arr in graphArr) {
            Graph[arr[0]].Add(arr[1]);
            Graph[arr[1]].Add(arr[0]);
        }
    }
}
/// <summary>DeepCopyするクラス</summary>
class DeepCopier {
    BinaryFormatter b = new BinaryFormatter();
    public T DeepCopy<T>(T obj) {
        T result;
        using (var mem = new MemoryStream()) {
            b.Serialize(mem, obj); //  binaryFormatterによりobjをmemにserial化して書き出す
            mem.Position = 0; // memのpotisionを先頭に戻す
            result = (T)b.Deserialize(mem); // memの内容を読み取る。
        }
        return result;
    }
}

static class MergeSort {
    public static long[] Sort(long[] arr) {
        return Sort(arr, 0, arr.Count());
    }

    // rightは+1されていることに注意
    private static long[] Merge(long[] sArr, int left, int mid, int right) {
        var n1 = mid - left;
        var n2 = right - mid;

        var lArr = new long[n1 + 1];
        var rArr = new long[n2 + 1];

        for (int i = 0; i < n1; i++) {
            lArr[i] = sArr[left + i];
        }
        lArr[n1] = int.MaxValue;

        for (int i = 0; i < n2; i++) {
            rArr[i] = sArr[mid + i];
        }
        rArr[n2] = int.MaxValue;

        int l = 0, r = 0;
        for (int k = left; k < right; k++) {
            if (lArr[l] <= rArr[r]) {
                sArr[k] = lArr[l];
                l++;
            } else {
                sArr[k] = rArr[r];
                r++;
            }
        }
        return sArr; // 要素数はright - left
    }

    private static long[] Sort(long[] sArr, int left, int right) {
        if (left + 1 < right) {
            var mid = (left + right) / 2;
            sArr = Sort(sArr, left, mid);
            sArr = Sort(sArr, mid, right);
            sArr = Merge(sArr, left, mid, right);
        }
        return sArr;
    }
}

/// <summary>あまりを計算するためのintのラッパー</summary>
struct ModInt {
    int Value { get; }
    int Mod { get; }

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

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

    public ModInt(long value, int mod = 1000000007) {
        this.Value = (int)(value % mod);
        this.Mod = mod;
    }

    public static explicit operator int(ModInt modInt) {
        return modInt.Value;
    }

    private static void CheckNotEqualMod(ModInt item1, ModInt item2) {
        if (item1.Mod != item2.Mod) {
            throw new Exception("mod not equal");
        }
    }

    public static ModInt operator +(ModInt item1, ModInt item2) {
        CheckNotEqualMod(item1, item2);
        long value = item1.Value + item2.Value;
        return new ModInt(value, item1.Mod);
    }

    public static ModInt operator *(ModInt item1, ModInt item2) {
        CheckNotEqualMod(item1, item2);
        long value = Math.BigMul(item1.Value, item2.Value);
        return new ModInt(value, item1.Mod);
    }

    public static ModInt operator -(ModInt item1, ModInt item2) {
        CheckNotEqualMod(item1, item2);
        long value = item1.Value - item2.Value;
        if (value < 0) {
            value += item1.Mod;
        }
        return new ModInt(value, item1.Mod);
    }

    public static ModInt operator +(ModInt item1, int item2) {
        return item1 + new ModInt(item2, item1.Mod);
    }

    public static ModInt operator *(ModInt item1, int item2) {
        return item1 * new ModInt(item2, item1.Mod);
    }

    public static ModInt operator -(ModInt item1, int item2) {
        return item1 - new ModInt(item2, item1.Mod);
    }


    public override int GetHashCode() {
        return this.Value;
    }

    public override bool Equals(object obj) {
        if (obj == null || this.GetType() != obj.GetType()) {
            return false;
        }

        var modIntObj = (ModInt)obj;
        return modIntObj.Value == this.Value;
    }

    public static bool operator ==(ModInt item1, ModInt item2) {
        return item1.Value == item2.Value;
    }

    public static bool operator !=(ModInt item1, ModInt item2) {
        return !(item1 == item2);
    }

    public static bool operator ==(ModInt item1, int item2) {
        return item1.Value == item2;
    }

    public static bool operator !=(ModInt item1, int item2) {
        return !(item1.Value == item2);
    }

    public static bool operator >=(ModInt item1, ModInt item2) {
        return item1.Value >= item2.Value;
    }

    public static bool operator <=(ModInt item1, ModInt item2) {
        return item1.Value <= item2.Value;
    }

    public static bool operator >=(ModInt item1, int item2) {
        return item1.Value >= item2;
    }

    public static bool operator <=(ModInt item1, int item2) {
        return item1.Value <= item2;
    }

    public static bool operator >(ModInt item1, ModInt item2) {
        return item1.Value > item2.Value;
    }

    public static bool operator <(ModInt item1, ModInt item2) {
        return item1.Value < item2.Value;
    }

    public static bool operator >(ModInt item1, int item2) {
        return item1.Value >= item2;
    }

    public static bool operator <(ModInt item1, int item2) {
        return item1.Value <= item2;
    }
}

/// <summary>組み合わせ</summary>
class ModCombination {
    private int mod;
    private int[] fac;
    private int[] finv;
    private int[] inv;

    public ModCombination(int max, int mod = 1000000007) {
        this.mod = mod;
        fac = new int[max]; // modが法のn!の列

        inv = new int[max]; // indexの逆元の列
        finv = new int[max]; // modを法とした、invの累積の累積

        fac[0] = 1; fac[1] = 1;
        finv[0] = 1; finv[1] = 1;
        inv[1] = 1;

        for (int i = 2; i < max; i++) {
            fac[i] = (int)(Math.BigMul(fac[i - 1], i) % mod);  // factorを求める
            var s = Math.BigMul(inv[mod % i], mod / i) % mod;
            inv[i] = (int)(mod - s);　 // iに対する逆元を求める
            finv[i] = (int)(Math.BigMul(finv[i - 1], inv[i]) % mod);
        }
    }
    /// <summary>nCk</summary>
    public int Calculation(int n, int k) {
        if (n < k) return 0;
        if (n < 0 || k < 0) return 0;

        return (int)(Math.BigMul(fac[n], (int)(Math.BigMul(finv[k], finv[n - k]) % mod)) % mod);
    }
}

/// <summary>拡張メソッドs</summary>
static class Extention {
    /// <summary>iとjを入れ替える</summary>
    public static void Swap<T>(this T[] arr, int i, int j) {
        var buf = arr[i];
        arr[i] = arr[j];
        arr[j] = buf;
    }

    /// <summary>
    /// partition。末尾sArr[r]を基準として、左に基準より小さい数、右に基準より大きい数が存在するように配列を並び替える。
    /// </summary>
    /// <param name="sArr"></param>
    /// <param name="p">partitionの先頭の添字</param>
    /// <param name="r">partitionの末尾の添字</param>
    /// <returns>partitionの基準が存在する添字</returns>
    public static int Partition(this int[] sArr, int p, int r) {
        var x = sArr[r];
        var i = p - 1;
        for (int j = p; j < r; j++) {
            if (sArr[j] <= x) {
                i++;
                sArr.Swap(i, j);
            }
        }
        sArr.Swap(i + 1, r);
        return i + 1;
    }

    /// <summary>深いコピーをする</summary>
    public static T DeepCopy<T>(this T obj) {
        T result;
        var b = new BinaryFormatter();
        using (var mem = new MemoryStream()) {
            b.Serialize(mem, obj); //  binaryFormatterによりobjをmemにserial化して書き出す
            mem.Position = 0; // memのpotisionを先頭に戻す
            result = (T)b.Deserialize(mem); // memの内容を読み取る。
        }
        return result;
    }

    public static string Left(this string str, int length) {
        return str.Substring(0, length);
    }

    public static string Right(this string str, int length) {
        return str.Substring(str.Length - length, length);
    }

    public static int IndexOf<T>(this T[] array, T obj) {
        return Array.IndexOf(array, obj);
    }
}