#include <bits/stdc++.h>
using namespace std;
int main()
  {int N; cin >> N;
  map<int, int64_t> m; vector<int> A(N); for (auto &a: A) {cin >> a; ++m[a];}
  int64_t s{}; for (auto [_, c] : m) s += c * (c - 1) / 2;
  for (int k = 0; k < N; ++k) {auto c{m[A[k]]}; cout << s - c * (c - 1) / 2 + (c - 1) * (c - 2) / 2 << "\n";}}
### Prompt

Create a solution in CPP for 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;
int main()
  {int N; cin >> N;
  map<int, int64_t> m; vector<int> A(N); for (auto &a: A) {cin >> a; ++m[a];}
  int64_t s{}; for (auto [_, c] : m) s += c * (c - 1) / 2;
  for (int k = 0; k < N; ++k) {auto c{m[A[k]]}; cout << s - c * (c - 1) / 2 + (c - 1) * (c - 2) / 2 << "\n";}}
```