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.

Examples

Input

5
1 1 2 1 2


Output

2
2
3
2
3


Input

4
1 2 3 4


Output

0
0
0
0


Input

5
3 3 3 3 3


Output

6
6
6
6
6


Input

8
1 2 1 4 2 1 4 1


Output

5
7
5
7
7
5
7
5
#include<bits/stdc++.h>
using namespace std;

#define i64 long long int
#define ran 202202

int n;
int a[ran];
int s[ran];

int main() {
	scanf("%d", &n);
	for(int i=0;i<n;i++) {
		scanf("%d", &a[i]);
		s[a[i]]++;
	}
	i64 ans = 0;
	for(int i=0;i<ran;i++)
		ans += 1LL*s[i]*(s[i]-1)/2;
	
	for(int i=0;i<n;i++) {
		printf("%lld\n", ans - (s[a[i]]-1));
	}
	
	return 0;
}