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
# coding: utf-8

n = input()
an = map(int, raw_input().split())

d = {}
for a in an:
    if not a in d:
        d[a] = 1
    else:
        d[a] += 1
#print d

sa = 0
for ai in d:
    si = d[ai] * (d[ai] - 1) // 2
    sa += si

for a in an:
    a1 = d[a] * (d[a] - 1) // 2
    a2 = (d[a] - 1) * (d[a] - 2) // 2

    print sa - a1 + a2
