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

int main(){
	long long n;	cin >> n;
	long long a[n];
	map <long long , long long> mp;
	for (int i = 0; i < n; ++i){
		cin >> a[i];
		mp[a[i]]++;
	}
	long long ans = 0;
	for(auto at : mp){
		ans += at.second * (at.second-1) / 2;
	}

	for (int i = 0; i < n; ++i){
		cout << ans - mp[a[i]] + 1 << endl;
	}

	return 0;
}
### Prompt

Your task is to create a cpp solution to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;

int main(){
	long long n;	cin >> n;
	long long a[n];
	map <long long , long long> mp;
	for (int i = 0; i < n; ++i){
		cin >> a[i];
		mp[a[i]]++;
	}
	long long ans = 0;
	for(auto at : mp){
		ans += at.second * (at.second-1) / 2;
	}

	for (int i = 0; i < n; ++i){
		cout << ans - mp[a[i]] + 1 << endl;
	}

	return 0;
}
```