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

long c2(long n) {
  return n * (n - 1) / 2;
}

int main() {
  int N;
  cin >> N;
  vector<int> A(N), cnt(N + 1);
  for (int i = 0, a; cin >> a; i++) A.at(i) = a, cnt.at(a)++;

  long sum = 0;
  for (int i : cnt) sum += c2(i);

  for (int a : A) cout << sum - c2(cnt.at(a)) + c2(cnt.at(a) - 1) << "\n";
}
### Prompt

Your challenge is to write 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
#include <bits/stdc++.h>
using namespace std;

long c2(long n) {
  return n * (n - 1) / 2;
}

int main() {
  int N;
  cin >> N;
  vector<int> A(N), cnt(N + 1);
  for (int i = 0, a; cin >> a; i++) A.at(i) = a, cnt.at(a)++;

  long sum = 0;
  for (int i : cnt) sum += c2(i);

  for (int a : A) cout << sum - c2(cnt.at(a)) + c2(cnt.at(a) - 1) << "\n";
}
```