Competitions

# Bracket sequence

The bracket sequence is a correct arithmetic expression, from which all numbers and signs are removed. For example,

1 + ( ( ( 2 + 3 ) + 5 ) + ( 3 + 4 ) )( ( ( ) ) ( ) )

#### Input

A sequence of opening and closing brackets is given. The length of the sequence is no more than 4000000.

#### Output

Print "YES" if the bracket sequence is correct and "NO" otherwise.

Time limit 4 seconds
Memory limit 128 MiB
Input example #1
((())())

Output example #1
YES

Input example #2
(()
Output example #2
NO