// D - Banned K
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i,n) for(int i=0;i<(n);++i)

int A[200000], C[200000];

int main(){
	int N; cin>>N;
	rep(i, N){ scanf("%d",A+i); A[i]--; C[A[i]]++; }//値の種類毎の計数
	ll all = 0; rep(a, N) all += (ll)C[a]*(C[a]-1)/2;//組み合わせの総計
	rep(k, N) printf("%lld\n",all - C[A[k]] + 1);
}
### 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
// D - Banned K
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i,n) for(int i=0;i<(n);++i)

int A[200000], C[200000];

int main(){
	int N; cin>>N;
	rep(i, N){ scanf("%d",A+i); A[i]--; C[A[i]]++; }//値の種類毎の計数
	ll all = 0; rep(a, N) all += (ll)C[a]*(C[a]-1)/2;//組み合わせの総計
	rep(k, N) printf("%lld\n",all - C[A[k]] + 1);
}
```