Balancing Parentheses

Only insertions of parentheses are allowed. Find the minimum number of insertions needed to turn the original string into a valid parenthesis string.

输入格式

One line containing a string of only ( and ), with full original bounds 1≤length≤100000.

输出格式

Output a single integer, the answer.

样例 1

输入：

()))

输出：

2

样例 2

输入：

))((

输出：

4

样例 3

输入：

()()

输出：

0

样例说明

The three examples need 2, 4, and 0 insertions respectively. The second can become (())(()); the source's (()))(()) is wrong in both length and validity and has been corrected.