The program reads from standard input a line containing an expression. Only round parentheses ( and ) are of interest; all other characters are ignored.
The depth of a parenthesis is the number of open parentheses that contain it, including itself. Print the maximum depth reached in the expression.
It is guaranteed that the parentheses are correctly matched (every ( has a matching ) and no ) appears before its corresponding open parenthesis).
The program reads from standard input a single line with the expression (at most 1000 characters long).
The program prints to standard output a single non-negative integer: the maximum nesting depth of the parentheses. If no parentheses appear in the expression, print `0`.
((a+b)*(c-(d+e)))
3
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((a+b)*(c-(d+e)))
3
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