E. Vanya and Bracketstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputVanya is doing his maths homework. He has an expression of form , where x1, x2, ..., xn are digits from 1 to 9, and sign  represents either a plus '+' or the multiplication sign '*'. Vanya needs to add one pair of brackets in this expression so that to maximize the value of the resulting expression.InputThe first line contains expression s (1 ≤ |s| ≤ 5001, |s| is odd), its odd positions only contain digits from 1 to 9, and even positions only contain signs  +  and  * . The number of signs  *  doesn't exceed 15.OutputIn the first line print the maximum possible value of an expression.ExamplesInput3+5*7+8*4Output303Input2+3*5Output25Input3*4*5Output60NoteNote to the first sample test. 3 + 5 * (7 + 8) * 4 = 303.Note to the second sample test. (2 + 3) * 5 = 25.Note to the third sample test. (3 * 4) * 5 = 60 (also many other variants are valid, for instance, (3) * 4 * 5 = 60).
Input3+5*7+8*4
Output303
['brute force', 'dp', 'expression parsing', 'greedy', 'implementation', 'strings', '*2100']