#include<iostream>
#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;

const int MAX_N = 200001;
int N, A[MAX_N], cnt[MAX_N];
int64_t ans;

int main() {
    cin >> N;
    rep(i, N) {
        cin >> A[i];
        ans += cnt[A[i]];
        cnt[A[i]]++;
    }
    rep(i, N) {
        cout << ans - cnt[A[i]] + 1 << endl;
    }
}
### Prompt

Please create a solution in CPP 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<iostream>
#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;

const int MAX_N = 200001;
int N, A[MAX_N], cnt[MAX_N];
int64_t ans;

int main() {
    cin >> N;
    rep(i, N) {
        cin >> A[i];
        ans += cnt[A[i]];
        cnt[A[i]]++;
    }
    rep(i, N) {
        cout << ans - cnt[A[i]] + 1 << endl;
    }
}
```