Given an array of ~n~ integers, count the number of subarrays where each element is distinct.

Input

• The first line has an integer ~n~: the array size.

The second line has ~n~ integers ~x\_1,x\_2,\dots,x\_n~: the array contents.

Output

• Print the number of subarrays with distinct elements.

Constraints

• ~1 \le n \le 2 \cdot 10^5~
• ~1 \le x\_i \le 10^9~

Example Input

4
1 2 1 3

Example Output

8

Explanation: The subarrays are ~[1]~ (two times), ~[2]~, ~[3]~, ~[1,2]~, ~[1,3]~, ~[2,1]~ and ~[2,1,3]~.