E - Vanya and Brackets CodeForces - 552E

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).

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <vector>
#include <queue>
#include <stack>
#include <map>

using namespace std;

typedef long long ll;
long long ans, t, n, m;
string str, s;
vector<int> vec;
stack<ll> sc, sn;
struct node {
    int x, y;
} no[2005];
long long result(long long a, long long b, char c) {
    return (c == '*') ? a * b : a + b;
}
void cal() {
    char t = sc.top();
    sc.pop();
    long long a = sn.top();
    sn.pop();
    long long b = sn.top();
    sn.pop();
    sn.push(result(a, b, t));
}
long long expression(string s) {
    for(int i = 0; i < s.size(); i++) {
        char c = s[i];
        if(isdigit(c)) {
            sn.push(c - '0');
        } else if(c == '(') {
            sc.push(c);
        } else if(c == ')') {
            while(sc.top() != '(') {
                cal();
            }
            sc.pop();
        } else {
            if(c == '+') {
                while(!sc.empty() && sc.top() == '*') {
                    cal();
                }
                sc.push(c);
            } else {
                sc.push(c);
            }
        }
    }
    while(!sc.empty()) {
        cal();
    }
    return sn.top();
}
int main() {
    cin >> str;
    n = str.size();
    vec.push_back(-1);
    for(int i = 1; i < n; i += 2) {
        if(str[i] == '*') {
            vec.push_back(i);
        }
    }
    vec.push_back(n);
    int len = vec.size();
    ans = 0;
    for(int i = 0; i < len - 1; i++) {
        for(int j = i + 1; j < len; j++) {
            s = str;
            s.insert(vec[i] + 1, 1, '(');
            s.insert(vec[j] + 1, 1, ')');
            ans = max(ans, expression(s));
        }
    }
    cout << ans << endl;
}