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.

Examples

Input

<>>

Output

3

Input

<>>><<><<<<<>>><

Output

28

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