LogiQuest

205. Longest Valid Parentheses

HardStack

Print the length of the longest valid (well-formed) parentheses substring.

Input format

A single line of ( and ) (it may be empty).

Output format

The length.

Example 1

Input

(()

Output

2

Example 2

Input

)()())

Output

4

Constraints

0 ≤ length ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 5 test cases, most of them hidden.

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