Problems
Bracket sequence
Bracket sequence
The bracket sequence is a correct arithmetic expression from which all numbers and operation signs have been removed. For example,
1 + ( ( ( 2 + 3 ) + 5 ) + ( 3 + 4 ) ) → ( ( ( ) ) ( ) )
Input data
A sequence of opening and closing brackets is given. The length of the sequence is no more than 4 \cdot 10^6.
Output data
Print "YES" if the bracket sequence is correct and "NO" otherwise.
Examples
Input example #1
((())())
Output example #1
YES
Input example #2
(()
Output example #2
NO