Score : $300$ points

Problem Statement

Given an array of $N$ integers $A=(A_1,A_2,...,A_N)$, find the number of pairs $(i,j)$ of integers satisfying all of the following conditions:

• $1 \le i < j \le N$
• $A_i \neq A_j$

Constraints

• All values in input are integers.
• $2 \le N \le 3 \times 10^5$
• $1 \le A_i \le 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the answer as an integer.

3
1 7 1

2

In this input, we have $A=(1,7,1)$.

• For the pair $(1,2)$, $A_1 \neq A_2$.
• For the pair $(1,3)$, $A_1 = A_3$.
• For the pair $(2,3)$, $A_2 \neq A_3$.

10
1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000

45

20
7 8 1 1 4 9 9 6 8 2 4 1 1 9 5 5 5 3 6 4

173