Every code editor can instantly tell you whether the brackets in your program match up. Tonight, you are the editor.
Given a string made of the characters ( and ), check if the brackets are balanced - every opening bracket is closed by exactly one closing bracket that comes after it, and every closing bracket closes exactly one opening bracket before it.
For example, (()()) is balanced, while (() is not (an opener was never closed) and )( is not (a closer appeared before any opener).
Input
First line of input will be a single string , made only of the characters ( and ).
Output
Print YES if the brackets are balanced, and NO otherwise.
Example
Input
(()())
Output
YES
The first bracket is closed by the last one, and the two pairs inside close each other.