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;
long f(long x){
    return x*(x-1)/2;
}
int main(void){
    long a,n; cin >> a;
    vector<int> v(200001);
    vector<int> w(a);
    for(int i=0;i<a;i++){
        cin >> n; v[n]++;
        w[i] = n;
    }
    long sum = 0;
    for(auto x:v)sum += f(x);
    for(auto y:w)cout << sum - f(v[y]) + f(v[y]-1) << endl;
}