#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int A[200005] , T[200005];
int main() {
    int N;
    cin >> N;
    ll ans = 0;
    for(int i = 0; i < N; i++){
        cin >> A[i];
        ans+=T[A[i]];
        T[A[i]]++;
    }
    for(int i = 0; i < N; i++){
        cout << ans - T[A[i]] + 1 << endl;
    }
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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;
using ll = long long;
int A[200005] , T[200005];
int main() {
    int N;
    cin >> N;
    ll ans = 0;
    for(int i = 0; i < N; i++){
        cin >> A[i];
        ans+=T[A[i]];
        T[A[i]]++;
    }
    for(int i = 0; i < N; i++){
        cout << ans - T[A[i]] + 1 << endl;
    }
}
```