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 Scala (2.13.1) (judge verdict: Accepted)

import scala.collection.mutable
import scala.collection.mutable.ArrayBuffer

object Main extends App {
  val sc = new FastScanner(System.in)
  val array = ArrayBuffer[Int]()
  val hashMap = mutable.HashMap[Int, Int]()
  val N: Int = sc.nextInt()
  1.to(N).foreach { _ =>
    val a = sc.nextInt()
    array.addOne(a)
    val count = hashMap.getOrElse(a, 0)
    hashMap.update(a, count + 1)
  }
  val patterns = (count: Long) => (count * (count - 1)) / 2
  val sum = hashMap.values.map { count => patterns(count) }.sum
  val cache = mutable.HashMap[Int, Long]()
  0.until(N).foreach { i =>
    val key = array(i)
    val result = cache.getOrElseUpdate(key,
      sum - patterns(hashMap(key)) + patterns(hashMap(key) - 1))
    println(result)
  }

  class FastScanner(in: java.io.InputStream) {
    val buffer = new Array[Byte](1024)
    var length = 0
    var p = 0

    def hasNextByte: Boolean =
      if (p < length) true
      else {
        p = 0
        length = in.read(buffer)
        if (length == 0) false else true
      }

    def readByte: Int = if (hasNextByte) buffer({ p += 1; p - 1 }) else -1

    def isPrintable(n: Int): Boolean = 33 <= n && n <= 126

    def skip(): Unit = while (hasNextByte && !isPrintable(buffer(p))) p += 1

    def hasNext: Boolean = {
      skip()
      hasNextByte
    }

    def next(): String = {
      if (!hasNext) throw new NoSuchElementException
      val sb = new java.lang.StringBuilder
      var temp = readByte
      while (isPrintable(temp)) {
        sb.appendCodePoint(temp)
        temp = readByte
      }
      sb.toString
    }

    def nextInt(): Int = Math.toIntExact(nextLong())

    def nextInts(n: Int): Array[Int] = {
      val ar = new Array[Int](n)
      for (i <- 0 until n) ar(i) = nextInt()
      ar
    }

    def nextLong(): Int = {
      if (!hasNext) throw new NoSuchElementException
      var minus = false
      var temp = readByte
      if (temp == '-') {
        minus = true
        temp = readByte
      }
      if (temp < '0' || '9' < temp) throw new NumberFormatException
      var n = 0
      while (isPrintable(temp)) {
        if ('0' <= temp && temp <= '9') {
          n *= 10
          n += temp - '0'
        }
        temp = readByte
      }
      if (minus) -n else n
    }
  }

}