Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5
1 1 2 1 2

Sample Output 1

2
2
3
2
3

Consider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.

From these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.

Thus, the answer for k=1 is 2.

Sample Input 2

4
1 2 3 4

Sample Output 2

0
0
0
0

No two balls have equal numbers written on them.

Sample Input 3

5
3 3 3 3 3

Sample Output 3

6
6
6
6
6

Any two balls have equal numbers written on them.

Sample Input 4

8
1 2 1 4 2 1 4 1

Sample Output 4

5
7
5
7
7
5
7
5

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.chomp.to_i
aa = gets.split.map(&:to_i)

len  = Array.new(n,0)
len2 = Array.new(n,0)
#1~nまで順番にその要素数を数え上げて
#各要素を格納する
n.times{ |l|
    count = aa.count(l+1)
    len[l] += count
}
#各要素が1こ減ったときの組み合わせ数を計算する
n.times{ |l|
    #初期化
    #l番目の要素が1個減った配列を用意
    tmp = len.dup
    total = 0
    if tmp[l] > 0  then tmp[l] -= 1 end
    #そもそも数値が現れなければ計算しない
    if tmp[l] != 0 then 
        n.times{ |m|
            if tmp[m] >= 2 then
                total += tmp[m]*(tmp[m]-1)/2
            end
        }
    end
    len2[l] = total
}
aa.each{ |bb|
    p len2[bb-1]
}