Problem:
Score : 400 points

Problem Statement

We have N balls. The i-th ball has an integer A_i written on it.

For each k=1, 2, ..., N, solve the following problem and print the answer.

Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.

Constraints

3 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

For each k=1,2,...,N, print a line containing the answer.

Sample Input 1

5
1 1 2 1 2

Sample Output 1

2
2
3
2
3

Consider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.

From these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.

Thus, the answer for k=1 is 2.

Sample Input 2

4
1 2 3 4

Sample Output 2

0
0
0
0

No two balls have equal numbers written on them.

Sample Input 3

5
3 3 3 3 3

Sample Output 3

6
6
6
6
6

Any two balls have equal numbers written on them.

Sample Input 4

8
1 2 1 4 2 1 4 1

Sample Output 4

5
7
5
7
7
5
7
5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.Set;

public class Main implements Runnable {
    public static void main(String[] args) {
        new Thread(null,new Main(), "" ,Runtime.getRuntime().maxMemory()).start();
    }

    public void run() {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int[] count = new int[2 * 10 * 10 * 10 * 10 * 10 + 5];
        int[] a = new int[n];
        Set<Integer> numSet = new HashSet<>();
        for(int i = 0;i < n;i++) {
            a[i] = sc.nextInt();
            count[a[i]]++;
            numSet.add(Integer.valueOf(a[i]));
        }

        PrintWriter out =  new PrintWriter(System.out);
        long[] memo = new long[2 * 10 * 10 * 10 * 10 * 10 + 5];
        Arrays.fill(memo, -1);
        for(int i = 0;i < n;i++) {
            if(memo[a[i]] == -1) {
                long ans = 0;
                for(Integer num : numSet) {
                    if(num.intValue() == a[i]) ans += nCm(count[a[i]] - 1, 2);
                    else ans += nCm(count[num.intValue()], 2);
                }
                memo[a[i]] = ans;
                out.println(ans);
            }
            else {
                out.println(memo[a[i]]);
            }
        }

        out.flush();
    }

    long nCm(int n, int m) {
        if(n < m) return 0l;
        long c = 1;
        m = (n - m < m ? n - m : m);
        for(int ns = n - m + 1, ms = 1;ms <= m;ns ++, ms++) {
            c *= ns;
            c /= ms;
        }
        return c;
    }

}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}