Parenthesis

Write a program that reads a sequence of lines, and for each line prints the number of clean parenthesized regions it contains.

A clean parenthesized region is a segment of the string that is immediatly after an open parenthesis, is immediately followed by a closed parenthesis, and contains no open or closed parenthesis.

For instance the substring "heha" is a clean parenthesized region in the string: "hello (heha) he said"
While in the string "hello (he(ha))) he said" the only clean parenthesized region corresponds to the substring "ha" since any larger parenthesized region contains other parenthesis.

Input

The input is a sequence of strings, each in one line.

Output

The output must contain, for each input line with at least one clean parenthesized region, the number of such regions in the line. Follow the format of the examples.

Problem information

Author: ProAl professors

Generation: 2026-01-25T16:53:19.678Z