#include<bits//stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define rep(i,n) for(int i = 0; i < n;i++)
int main() {
	int n;cin >> n;ll sum = 0;
	vector<ll> a(n),c(n,0);
	rep(i, n) {
		cin >> a[i];a[i]--;
		c[a[i]]++;
	}
	rep(i, n) sum += c[i] * (c[i] - 1) / 2;
	rep(i,n) cout << sum - c[a[i]] + 1 << endl;
}
### Prompt

Please formulate 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;
typedef long long ll;
typedef long double ld;
#define rep(i,n) for(int i = 0; i < n;i++)
int main() {
	int n;cin >> n;ll sum = 0;
	vector<ll> a(n),c(n,0);
	rep(i, n) {
		cin >> a[i];a[i]--;
		c[a[i]]++;
	}
	rep(i, n) sum += c[i] * (c[i] - 1) / 2;
	rep(i,n) cout << sum - c[a[i]] + 1 << endl;
}
```