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.

4
3 1 4 1

2

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

10
99999 99998 99997 99996 99995 99994 99993 99992 99991 99990

120

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

355