#include <bits/stdc++.h>
using namespace std;

int main() {
  int64_t N,ans=0;
  cin >> N;
  vector<int64_t>A(N);
  vector<int64_t>B(N+1,0);
  for(int i=0;i<N;i++){
    cin >> A.at(i);
    B.at(A.at(i))++;
  }
  for(int i=1;i<=N;i++){
    ans+=(B.at(i)*(B.at(i)-1))/2;
  }
  for(int i=0;i<N;i++){
    cout << ans-B.at(A.at(i))+1 << endl;
  }
}
### Prompt

Develop a solution in Cpp to the problem described below:

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;

int main() {
  int64_t N,ans=0;
  cin >> N;
  vector<int64_t>A(N);
  vector<int64_t>B(N+1,0);
  for(int i=0;i<N;i++){
    cin >> A.at(i);
    B.at(A.at(i))++;
  }
  for(int i=1;i<=N;i++){
    ans+=(B.at(i)*(B.at(i)-1))/2;
  }
  for(int i=0;i<N;i++){
    cout << ans-B.at(A.at(i))+1 << endl;
  }
}
```