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#F1640. Vanya and Brackets

    ID: 1646 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 7 上传者: 标签>枚举动态规划表达式解析贪心模拟字符串算法思想编程与模拟提高难度共享题库Codeforces英文题面题目来源题面语言

Vanya and Brackets

题目描述

E. Vanya and Brackets
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Vanya 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.

Input

The 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.

Output

In the first line print the maximum possible value of an expression.

Examples
Input
3+5*7+8*4
Output
303
Input
2+3*5
Output
25
Input
3*4*5
Output
60
Note

Note 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).

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1166 题。保留原作者与原赛事署名。