Given an integer array $A$ of length $n$. Count the number of subarray contain only unique elements (i.e. no value appears more than once).

For example, ${3, 2, 3}$ is not sastified because value $3$ appears 2 times.

Input

• The first line contains an integers $n$.
• The second line contains $n$ integers $A_i$.

Output

• Print the number of unique subarrays.

Constraints

• $1 \le n \le 10^5$.
• $1 \le A_i \le 10^5$.

Example

Input:

4
1 2 1 2

Output:

7