Description

Hecy has taken on a new task: BE processing. There is a category in BE called GBE.

The definition of GBE is as follows:

1. An empty expression is a GBE.
2. If expression A is a GBE, then [A] and (A) are both GBEs.
3. If A and B are both GBEs, then AB is a GBE.

Given a BE, determine the minimum number of characters that need to be added to make this BE a GBE.

Input Format

The input consists of a single line, the string BE.

Output Format

Output a single integer, representing the minimum number of characters to be added.

Sample 1

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1

Data Range and Hint

For $100\%$ of the data, the length of the input string is less than $100$.