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;
typedef long long ll;
typedef pair<int,int> P;
ll n;
ll a[200005],b[200005];
ll A[200005];
ll ANS;
int main(void){
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
		b[a[i]]++;
	}
	for(int i=1;i<=n;i++){
		A[i]=b[i]*(b[i]-1)/2;
		ANS+=A[i];
	}
	for(int i=0;i<n;i++){
		cout<<ANS-A[a[i]]+(b[a[i]]-1)*(b[a[i]]-2)/2<<endl;
	}
	
}
