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 OCaml (4.02.3) (judge verdict: Accepted)

open Batteries
module CountDict = Map.Make(Int)
let count_int lst =
  let rec add_lst dict l =
    match l with
    | [] -> dict
    | first :: rest ->
      if CountDict.mem first dict then add_lst (CountDict.add first ((CountDict.find first dict) + 1) dict) rest else
      add_lst (CountDict.add first 1 dict) rest
  in add_lst CountDict.empty lst

let n = read_int ()
let a = read_line () |> String.split_on_char ' ' |> List.map int_of_string

let dict = count_int a

let all = (CountDict.fold (fun key value a -> a + (value * (value - 1))) dict 0) / 2

let rec loop lst =
  match lst with
  | [] -> ()
  | first :: rest -> let value = CountDict.find first dict in Printf.printf "%d\n" (all - value + 1); loop rest

let _ = loop a