#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int>P;
#define F first
#define S second
int INF=1e9;
string s;
P init=P(INF,-INF);
vector<vector<P> >dp(200,vector<P>(200,init));

P dfs(int l,int r){
	if(l==r)return P(s[l]-'0',s[l]-'0');
	if(dp[l][r]!=init)return dp[l][r];
	P res=init;
	if(s[l]=='('&&r-l>2) res=dfs(l+1,r);
	if(s[r]==')'&&r-l>2) res=dfs(l,r-1);
	for(int i=l+1;i<r;i++){
		if(!(s[i]=='-'||s[i]=='+'))continue;
		P a=dfs(l,i-1);
		P b=dfs(i+1,r);
		if(s[i]=='-'){
			res.F=min(res.F,a.F-b.S);
			res.S=max(res.S,a.S-b.F);
		}
		if(s[i]=='+'){
			res.F=min(res.F,a.F+b.F);
			res.S=max(res.S,a.S+b.S);
		}
	}
	return dp[l][r]=res;
}

int main(){
	cin>>s;
	cout<<dfs(0,s.size()-1).S<<endl;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

Tunnel formula

One day while exploring an abandoned mine, you found a long formula S written in the mine. If you like large numbers, you decide to take out the choke and add `(` or `)` so that the result of the formula calculation is as large as possible. If it has to be a mathematical formula even after adding it, how many can it be at the maximum?

There is enough space between the letters, and you can add as many `(` or `)` as you like. If the final formula is a formula, you may write `(` or `)` so that the correspondence of the first parenthesis is broken (see Sample 2). Also, here, <expr> defined by the following BNF is called a mathematical formula. All numbers in the formula are single digits.


<expr> :: = "(" <expr> ")"
| <term> "+" <term>
| <term> "-" <term>
<term> :: = <digit> | <expr>
<digit> :: = "0" | "1" | "2" | "3" | "4"
| "5" | "6" | "7" | "8" | "9"


Constraints

* 3 ≤ | S | ≤ 200



S represents a mathematical formula.

Input Format

Input is given from standard input in the following format.


S


Output Format

Output the answer as an integer.

Sample Input 1


1- (2 + 3-4 + 5)


Sample Output 1


Five


1- (2 + 3- (4 + 5)) is the maximum.

Sample Input 2


1- (2 + 3 + 4)


Sample Output 2


0


(1- (2 + 3) + 4) is the maximum.

Sample Input 3


1- (2 + 3)


Sample Output 3


-Four


Note that 1- (2) + (3) is not the formula here.





Example

Input

1-(2+3-4+5)


Output

5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int>P;
#define F first
#define S second
int INF=1e9;
string s;
P init=P(INF,-INF);
vector<vector<P> >dp(200,vector<P>(200,init));

P dfs(int l,int r){
	if(l==r)return P(s[l]-'0',s[l]-'0');
	if(dp[l][r]!=init)return dp[l][r];
	P res=init;
	if(s[l]=='('&&r-l>2) res=dfs(l+1,r);
	if(s[r]==')'&&r-l>2) res=dfs(l,r-1);
	for(int i=l+1;i<r;i++){
		if(!(s[i]=='-'||s[i]=='+'))continue;
		P a=dfs(l,i-1);
		P b=dfs(i+1,r);
		if(s[i]=='-'){
			res.F=min(res.F,a.F-b.S);
			res.S=max(res.S,a.S-b.F);
		}
		if(s[i]=='+'){
			res.F=min(res.F,a.F+b.F);
			res.S=max(res.S,a.S+b.S);
		}
	}
	return dp[l][r]=res;
}

int main(){
	cin>>s;
	cout<<dfs(0,s.size()-1).S<<endl;
}

```