#include<iostream>
using namespace std;
const int N=2e5+10;
long long a[N],b[N];
int main(){
	int n;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
		b[a[i]]++;
	}
	long long sum=0;
	for(int i=0;i<=n;i++) sum+=(b[i]*(b[i]-1))/2;
	for(int i=0;i<n;i++){
		long long res=sum-b[a[i]]*(b[a[i]]-1)/2+(b[a[i]]-1)*(b[a[i]]-2)/2;
		cout<<res<<"\n";
	}
	return 0;
}

### Prompt

In Cpp, your task is to solve 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<iostream>
using namespace std;
const int N=2e5+10;
long long a[N],b[N];
int main(){
	int n;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
		b[a[i]]++;
	}
	long long sum=0;
	for(int i=0;i<=n;i++) sum+=(b[i]*(b[i]-1))/2;
	for(int i=0;i<n;i++){
		long long res=sum-b[a[i]]*(b[a[i]]-1)/2+(b[a[i]]-1)*(b[a[i]]-2)/2;
		cout<<res<<"\n";
	}
	return 0;
}

```