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<iostream>
#include<cstdio>
using namespace std;
const int N = 2e5 + 10;
int n, a[N];
long long sum[N], tot;
int main() {
    scanf("%d", &n);
    for(int i=1;i<=n;i++)scanf("%d", &a[i]),sum[a[i]]++;
    for(int i=1;i<=n;i++)tot+=sum[i]*(sum[i]-1)/2;
    for(int i=1;i<=n;i++)printf("%lld\n",tot-(sum[a[i]]-1));
    return 0;
}