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,
$$
1 + ( ( ( 2 + 3 ) + 5 ) + ( 3 + 4 ) ) → ( ( ( ) ) ( ) )
$$
\InputFile
A sequence of opening and closing brackets is given. The length of the sequence is no more than $4 \cdot 10^6$.
\OutputFile
Print \textbf{"YES"} if the bracket sequence is correct and \textbf{"NO"} otherwise.
Input example #1
((())())
Output example #1
YES
Input example #2
(()
Output example #2
NO