#include <bits/stdc++.h>
 
int cnt[200001];
 
using namespace std;
 
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int &p : a) cin >> p;
  for (int p : a) ++cnt[p];
  long long ans = 0;
  for (int i = 1; i <= 200000; ++i) {
    ans += 1LL * cnt[i] * (cnt[i] - 1) / 2;
  }
  for (int p : a) {
  	cout << ans - cnt[p] + 1 << '\n';
  }
  return 0;
}
### 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 <bits/stdc++.h>
 
int cnt[200001];
 
using namespace std;
 
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int &p : a) cin >> p;
  for (int p : a) ++cnt[p];
  long long ans = 0;
  for (int i = 1; i <= 200000; ++i) {
    ans += 1LL * cnt[i] * (cnt[i] - 1) / 2;
  }
  for (int p : a) {
  	cout << ans - cnt[p] + 1 << '\n';
  }
  return 0;
}
```