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.

Sample Input 1

3

1 7 1

Sample Output 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 $(2,3)$, $A\_2 \neq A\_3$.

Sample Input 2

10

1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000

Sample Output 2

45

Sample Input 3

20

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

Sample Output 3

173