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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import math
import copy
from copy import deepcopy
import sys
import fractions
# import numpy as np
from functools import reduce
# import statistics
import decimal
import heapq
import collections
import itertools

sys.setrecursionlimit(100001)


# input = sys.stdin.readline
# sys.setrecursionlimit(10**6)

# ===FUNCTION===

def getInputInt():
    inputNum = int(input())
    return inputNum


def getInputListInt():
    outputData = []
    inputData = input().split()
    outputData = [int(n) for n in inputData]

    return outputData


def getSomeInputInt(n):
    outputDataList = []
    for i in range(n):
        inputData = int(input())
        outputDataList.append(inputData)

    return outputDataList


def getSomeInputListInt(n):
    inputDataList = []
    outputDataList = []
    for i in range(n):
        inputData = input().split()
        inputDataList = [int(n) for n in inputData]
        outputDataList.append(inputDataList)

    return outputDataList


# ===CODE===

n = int(input())
d = getInputListInt()


def combinations_count(n, r):
    if n <= 1:
        return 0
    else:
        return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

dic = {}
dic_ans = {}
dic_comb = {}

for key in d:
    if key in dic:
        dic[key] += 1
    else:
        dic[key] = 1

tmp_keys = []
for key in dic:
    if dic[key] < 2:
        tmp_keys.append(key)

for k in tmp_keys:
    del dic[k]

tmp_len = len(dic)

for i in range(n):
    ans = 0
    tmp_key = d[i]

    if tmp_len == 0:
        print(0)
        continue

    if tmp_key in dic_ans:
        print(dic_ans[tmp_key])
    else:
        for k in dic:
            if k == tmp_key:
                tmp_dic_idx = dic[k]-1
                if tmp_dic_idx in dic_comb:
                    ans += dic_comb[tmp_dic_idx]
                else:
                    tmp_calc = combinations_count(tmp_dic_idx, 2)
                    ans += tmp_calc
                    dic_comb[tmp_dic_idx] = tmp_calc
            else:
                tmp_dic_idx = dic[k]
                if tmp_dic_idx in dic_comb:
                    ans += dic_comb[tmp_dic_idx]
                else:
                    tmp_calc = combinations_count(tmp_dic_idx, 2)
                    ans += tmp_calc
                    dic_comb[tmp_dic_idx] = tmp_calc
        print(ans)
        dic_ans[tmp_key] = ans