You are given a string $S$, which is balanced parentheses with a star symbol '*' inserted.

Any balanced parentheses can be constructed using the following rules:

* An empty string is balanced.
* Concatenation of two balanced parentheses is balanced.
* If $T$ is balanced parentheses, concatenation of '(', $T$, and ')' in this order is balanced.



For example, '()()' and '(()())' are balanced parentheses. ')(' and ')()(()' are not balanced parentheses.

Your task is to count how many matching pairs of parentheses surround the star.

Let $S_i$be the $i$-th character of a string $S$. The pair of $S_l$ and $S_r$ ($l < r$) is called a matching pair of parentheses if $S_l$ is '(', $S_r$ is ')' and the surrounded string by them is balanced when ignoring a star symbol.



Input

The input consists of a single test case formatted as follows.


$S$


$S$ is balanced parentheses with exactly one '*' inserted somewhere. The length of $S$ is between 1 and 100, inclusive.

Output

Print the answer in one line.

Examples

Input

((*)())


Output

2


Input

(*)


Output

1


Input

(()())*


Output

0


Input

()*()


Output

0


Input

((((((((((*))))))))))


Output

10


Input

*


Output

0
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>

using namespace std;

//conversion
//------------------------------------------
inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}

//math
//-------------------------------------------
template<class T> inline T sqr(T x) {return x*x;}

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//repetition
//------------------------------------------
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,n)  FOR(i,0,n)

//constant
//--------------------------------------------
const double PI  = acos(-1.0);

//clear memory
#define CLR(a) memset((a), 0 ,sizeof(a))

//debug
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
int main(){
       string s;
       cin >> s;
       int st = s.find('*');
       int rr=0, r=0, l=0, ll=0, ans;
       ll = s.find( '(');
       rr = s.rfind(')');
       
       for(int i = ll; i < st; i++){
           if(s[i]=='(') l++;
           if(s[i]==')') l--;
       }
       for(int i = st+1; i <=rr; i++){
           if(s[i]==')') r++;
           if(s[i]=='(') r--;
       }
       if(r<=l) ans = r;
       else ans = l;
       if(ans<=0) ans=0;
       cout << ans << endl;
       
}
