Remove the parentheses#4437

Remove the parentheses

1 second
128 megabytes
Very easy

Given a string consisting of parentheses.

Determine the minimum number of characters to be removed from this string, so that the remaining characters will form the correct bracket sequence.

Input

One line consisting of no more than 10^5 parentheses.

Output

Print a single number — the answer to the problem.

Examples

Example 1

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Example 2

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Example 3

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