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.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分