Problem Statement

Given is a string $S$ of length $N-1$. Each character in $S$ is < or >.

A sequence of $N$ non-negative integers, $a_1,a_2,\cdots,a_N$, is said to be good when the following condition is satisfied for all $i$ ($1 \leq i \leq N-1$):

• If $S_i=$ <: $a_i<a_{i+1}$
• If $S_i=$ >: $a_i>a_{i+1}$

Find the minimum possible sum of the elements of a good sequence of $N$ non-negative integers.

Constraints

• $2 \leq N \leq 5 \times 10^5$
• $S$ is a string of length $N-1$ consisting of < and >.

Input

Input is given from Standard Input in the following format:

S

Output

Find the minimum possible sum of the elements of a good sequence of $N$ non-negative integers.