Competitions

# Stack Data Structure

# 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.

Input example #1

((())())

Output example #1

YES

Input example #2

(()

Output example #2

NO