Given an array $A$ of $n$ integers. Count the number of contiguous subsequences such that all values in the subsequence appear an odd number of times.

Input

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

Output

• Print an integer, the number of subsequences that satisfy the condition.

Constraints

• $1 \le n,A_i \le 10^5$.

Example

Input:

3
1 2 2

Output:

4