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: Wrong Answer)

import java.util.*;

public class Main {
    static int MAX = 200001;  // (1 ≦ k ≦ n ≦ 10^7 程度)
    static int MOD = 1000000007;
    static long[] fac;  // 階乗
    static long[] finv;
    static long[] inv;  // 逆元
    
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = sc.nextInt();
        }
        
        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
            int key = array[i];
            if (!map.containsKey(key)) {
                map.put(key, 1);
            } else {
                int val = map.get(key);
                map.put(key, val + 1);
            }
        }
        
        COMinit();
        
        for (int i = 0; i < n; i++) {
            long ans = 0;
            int num = array[i];
            
            for (Integer key : map.keySet()) {
                int val = map.get(key);
                if (key == num) val--;
                
                ans += nCkMOD(val, 2);
            }
            System.out.println(ans);
        }
        
    }
    
    // テーブルを作る前処理
    public static void COMinit() {        
        fac = new long[MAX];
        finv = new long[MAX];
        inv = new long[MAX];
        
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for (int i = 2; i < MAX; i++){
            fac[i] = fac[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
    }
    
    // 二項係数計算(1 ≦ k ≦ n ≦ 10^7 程度)
    public static long nCkMOD(int n, int k){
        if (n < k) return 0;
        if (n < 0 || k < 0) return 0;
        return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
    }
    
    public static long modpow(long a, long n) {
        long res = 1;
        while (n > 0) {
            long tmp = n & 1;
            if (tmp > 0) res = res * a % MOD;
            a = a * a % MOD;
            n >>= 1;
        }
        return res;
    }
}