#include<bits/stdc++.h>
using namespace std;
long long a[200005],b[200005],c,x=0;
int main()
{
	long long n,i;
	scanf("%lld",&n);
	for(i=0;i<n;i++)
	{
		scanf("%lld",&a[i]);
		b[a[i]]++;
	}
	for(i=1;i<=200000;i++)
	{
		if(b[i])
		{
			int c=b[i];
			c--;
			while(c)
			{
				x+=c;
				c--;
			}
		}
	}
	for(i=0;i<n;i++)
	{
		printf("%lld\n",x-b[a[i]]+1);
	}
} 
### Prompt

Generate 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;
long long a[200005],b[200005],c,x=0;
int main()
{
	long long n,i;
	scanf("%lld",&n);
	for(i=0;i<n;i++)
	{
		scanf("%lld",&a[i]);
		b[a[i]]++;
	}
	for(i=1;i<=200000;i++)
	{
		if(b[i])
		{
			int c=b[i];
			c--;
			while(c)
			{
				x+=c;
				c--;
			}
		}
	}
	for(i=0;i<n;i++)
	{
		printf("%lld\n",x-b[a[i]]+1);
	}
} 
```