Find the longest valid bracket sequence

The C++ programming language uses curly braces { and } to separate scopes. You’re trying to parse a C++ code and would like to make sure it’s syntactically correct. The first step is to make sure the opening curly braces match the closing ones.
You’ve decided to write a program that given a list of curly braces would print the longest sequence of curly braces starting from the very beginning that’s valid.

Input

The only line of the input contains a string b (1 ≀ |b| ≀ ) containing curly braces.

Output

The program should print the length of the longest sequence of curly braces that’s valid and starts from the beginning.

Examples

Input
Output
{{}}
4
{{{}
0
}{{}
0
{}{{{{}
2
Β 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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