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:

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

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分