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. 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