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.