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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.math.BigInteger;
import java.util.*;


public class Main {

    private static List<List<Integer>> subsets;
    private static int count = 0;
    private static BigInteger thirteen = new BigInteger("13");
    private static BigInteger five = new BigInteger("5");
    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        InputReader.OutputWriter out = new InputReader.OutputWriter(outputStream);

        int n = in.nextInt();
        String [] a = new String[n];
        for (int i = 0; i < n; i++) {
            char [] c  = in.next().toCharArray();
            Arrays.sort(c);
            a[i] = new String(c);
        }
        Arrays.sort(a);
        long ans = 0;
        String current = a[0];
        long count = 1;
        for (int i = 1; i < a.length; i++) {
            if(a[i].equals(current)) {
                count++;
            }
            else {
                ans+=count*(count-1)/2;
                count = 1;
                current = a[i];
            }
        }
        ans+=count*(count-1)/2;
        out.println(ans);
        out.flush();
    }
    private static void dfs(int[][] grid, int i, int j, boolean[][] visited, boolean[][] changed) {
        if(i<0 || i>=grid.length || j<0 || j>=grid[0].length || visited[i][j]) {
            return;
        }
        visited[i][j] = true;
        if(grid[i][j] == 1) {
            if(!isBorder(grid,i,j,changed)) {
                grid[i][j] = 0;
                changed[i][j] = true;
            }
        }
        dfs(grid,i+1,j,visited,changed);
        dfs(grid,i-1,j,visited,changed);
        dfs(grid,i,j + 1,visited,changed);
        dfs(grid,i,j - 1,visited,changed);
    }
    static boolean isBorder(int [][] grid, int i, int j, boolean[][] changed) {
        if (i - 1 < 0) return true;
        if (i + 1 == grid.length) return true;
        if (j - 1 < 0) return true;
        if (j + 1 == grid[0].length) return true;
        if(grid[i-1][j-1] == 0 && !changed[i-1][j-1]) return true;
        if(grid[i-1][j] == 0 && !changed[i-1][j]) return true;
        if(grid[i+1][j] == 0 && !changed[i+1][j]) return true;
        if(grid[i][j-1] == 0 && !changed[i][j-1]) return true;
        if(grid[i][j+1] == 0 && !changed[i][j+1]) return true;
        return false;
    }
    static boolean check(int [][] grid, int i, int j) {
        return i>=0 && j>=0 && i < grid.length && j<grid[0].length;
    }
    static int toDecany(String s) {
        char [] c = s.toCharArray();
        int ans = 0;
        int k = 0;
        for (int i = c.length - 1; i >=0; i--) {
            int value = (c[i]-'0');
            ans+=value*Math.pow(2,k++);
        }
        return ans;
    }

    static void generate(char [] c, int index) {
        if(index == c.length) {
            BigInteger b = new BigInteger(new String(c));
            if(b.mod(thirteen).equals(five)) {
                count = (count + 1)%1000000007;
            }
            return;
        }
        if(c[index] == '?') {
            for (char i = '0'; i <= '9'; i++) {
                if(c[index] == '?') {
                    c[index] = i;
                    generate(c, index + 1);
                    c[index] = '?';
                }
            }
        }
        else {
            generate(c,index + 1);
        }



    }
    public boolean possibleBipartition(int n, int[][] dislikes) {
        HashMap<Integer,Set<Integer>> map = mapToDislikes(dislikes);
        HashSet<Integer> first = new HashSet<>();
        HashSet<Integer> second = new HashSet<>();
        for(Map.Entry<Integer,Set<Integer>> m : map.entrySet()) {
            Set<Integer> set = m.getValue();
            boolean found = false;
            for(int i : set) {
                if(first.contains(i)) {
                    found = true;
                    break;
                }
            }
            if(!found) first.add(m.getKey());
            else {
                found = false;
                for(int i : set) {
                    if(second.contains(i)) {
                        found = true;
                        break;
                    }
                }
                if(found) return true;
                else second.add(m.getKey());
            }
        }
        return true;
    }
    private HashMap<Integer,Set<Integer>> mapToDislikes(int [][] dislakes) {
        HashMap<Integer,Set<Integer>> map = new HashMap<>();
        for(int [] i : dislakes) {
            addToMap(i[0],i[1],map);
            addToMap(i[1],i[0],map);
        }
        return map;
    }
    private void addToMap(int key, int value, HashMap<Integer,Set<Integer>> map) {
        Set<Integer> set;
        if(map.containsKey(key)) {
            set = map.get(key);
        }
        else {
            set = new HashSet<>();
        }
        set.add(value);
        map.put(key,set);
    }
    static int toBinary(int n) {
        String  s = Integer.toBinaryString(n);
        return Integer.parseInt(s);
    }
    static int numberOfDigits(int n) {
        int count = 0;
        while (n>0) {
            n/=10;
            count++;
        }
        return count;
    }
    static int gcd(int a,int b) {
        return b == 0 ? a : gcd(b,a%b);
    }
    static char [] convert(char [] c) {
        for (int i = 0; i < c.length; i++) {
            char current = c[i];
            if (current == '9') {
                c[i] = '0';
            }
            else {
                c[i] = ++c[i];
            }
        }
        return c;
    }
    static char [] shift(char [] c) {
        char temp = c[c.length - 1];
        for (int i = 0; i < c.length;i++) {
            char current = c[i];
            c[i] = temp;
            temp = current;
        }
        c[0] = temp;
        return c;
    }
    static void subsets(int [] a, int index, List<Integer> list) {
        subsets.add(new ArrayList<>(list));
        for (int i = index; i < a.length; i++) {
            list.add(a[i]);
            subsets(a,i+1,list);
            list.remove(list.size() - 1);
        }
    }
    static long sum(long n) {
        return n*(n+1)/2;
    }

    static int lcm(int a,int b,int gcd) {
        return a*b/gcd;
    }

}
class Point {
    int x;
    int y;
    public int getX() {
        return x;
    }
    public int getY() {
        return y;
    }
    public Point(int x,int y) {
        this.x = x;
        this.y = y;
    }
}
class InputReader extends BufferedReader {
    StringTokenizer tokenizer;

    public InputReader(InputStream inputStream) {
        super(new InputStreamReader(inputStream), 32768);
    }

    public InputReader(String filename) {
        super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(readLine());
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }
        return tokenizer.nextToken();
    }
    public Integer nextInt() {return Integer.valueOf(next());}
    public Long nextLong() {return  Long.valueOf(next());}
    public Double nextDouble() {return Double.valueOf(next());}

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }
    }
}