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Contest: Task: Related: TaskC TaskE

Score : $400$ points

Problem Statement

You are given a sequence of length $N$: $A=(A_1,A_2,\ldots,A_N)$.
Find the number of triples $(i,j,k)$ that satisfy both of the following conditions.

  • $1\leq i \lt j \lt k \leq N$
  • $A_i$, $A_j$, and $A_k$ are distinct.

Constraints

  • $3 \leq N \leq 2\times 10^5$
  • $1 \leq A_i \leq 2\times 10^5$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

4
3 1 4 1

Sample Output 1

2

The two triples $(i,j,k)$ satisfying the conditions are $(1,2,3)$ and $(1,3,4)$.

Sample Input 2

10
99999 99998 99997 99996 99995 99994 99993 99992 99991 99990

Sample Output 2

120

Sample Input 3

15
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9

Sample Output 3

355