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A sequence of brackets is called balanced if one can turn it into a valid math expression by adding characters «+» and «1». For example, sequences «(())()», «()» and «(()(()))» are balanced, while «)(», «(()» and «(()))(» are not.

You are given a string which consists of opening and closing round brackets. Check whether it is a balanced bracket sequence.

Input

The only line of input contains a string between 1 and 100 characters long, inclusive. Each character in the string will be «(» or «)».

Balanced brackets

Examples