CF552E · Vanya and Brackets

• 难度：2100
• 标签：brute force、dp、expression parsing、greedy、implementation、strings
• 链接：https://codeforces.com/problemset/problem/552/E
• 时间限制：1 second　内存限制：256 megabytes
• 出现位置：Day02-表达式解析-栈-括号序列/选做；Day30-结营-个人错题重做-公共重测池-尖子拔高

英文原题面

Statement

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.

样例

样例 1

输入：

3+5*7+8*4

输出：

303

样例 2

输入：

2+3*5

输出：

25

样例 3

输入：

3*4*5

输出：

60

样例解释（英文原文）

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).