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.

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

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