Balanced Expressions

Background

   Let us consider expressions formed by nonnegative integers, the unary operator "-", the binary operators "+", "-", "*" and "/" and the symbols "( " and ")".
   Two expressions E and F are isomorphic if E can be obtained from F by replacing some nonnegative integers by others. The expressions (2+3) * 6 - (-4) and (7+0) * 6 - (-8) are isomorphic, but neither of them is isomorphic to (-2 +3) * 6 - (-4).
   An expression E is balanced if every binary operation in it is applied to two isomorphic expressions. The expressions -5, (1+2) * (3+5) and ((-3)/( -4))/(( -1)/( -100)) are balanced, while 12 + (3-2) is not.

Problem

   Given an expression E, check whether it is balanced.

Input

   The input consists of several lines with the expressions to be tested, one per line.

Output

   The output consists of a separated line for each expression with a single word, either YES or NO.

Sample Input
(1+2) * (3+5)

Sample Output
YES