#include <bits/stdc++.h>
const int N = 2e5 + 54;
int n, a[N], s[N];
long long ans;
int main() {
	std::cin >> n;
	for (int i = 1; i <= n; ++i) std::cin >> a[i], ++s[a[i]];
	for (int i = 1; i <= n; ++i) 
		if (s[i]) ans += (long long) s[i] * (s[i] - 1) / 2;
	for (int i = 1; i <= n; ++i) {
		std::cout << ans - s[a[i]] + 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>
const int N = 2e5 + 54;
int n, a[N], s[N];
long long ans;
int main() {
	std::cin >> n;
	for (int i = 1; i <= n; ++i) std::cin >> a[i], ++s[a[i]];
	for (int i = 1; i <= n; ++i) 
		if (s[i]) ans += (long long) s[i] * (s[i] - 1) / 2;
	for (int i = 1; i <= n; ++i) {
		std::cout << ans - s[a[i]] + 1 << '\n';
	}
}

```