Codeforces Round #416 (Div. 2) has been moved to start on 27.05.2017 09:35 (UTC). ×

H. Balanced brackets
time limit per test
2 seconds
memory limit per test
64 megabytes
input
standard input
output
standard output

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 «)».

Output

Output «YES» if the bracket sequence is balanced, and «NO» otherwise (quotes for clarity only).

Examples
Input
(()(()))()
Output
YES
Input
())()
Output
NO