Problem Statement

You are given a string $S$ of length $N-1$ consisting of < and >.

A sequence $x=(x_1,x_2,\cdots,x_N)$ of length $N$ is called a good sequence if and only if it satisfies the following condition:

• For each $i$ ($1 \leq i \leq N-1$), if the $i$-th character of $S$ is <, then $x_i\lt x_{i+1}$; if it is >, then $x_i \gt x_{i+1}$.

Find the minimum possible inversion number of a good sequence.

What is the inversion number of a sequence? The inversion number of a sequence $x=(x_1,x_2,\cdots,x_n)$ of length $n$ is the number of pairs of integers $(i,j)$ ($1 \leq i < j \leq n$) such that $x_i>x_j$.

Constraints

• $2 \leq N \leq 250000$
• $S$ is a string of length $N-1$ consisting of < and >.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
S

Output

Print the answer.