Nurzhan Yergozhin (guess)
Submitted: Sat, Nov 17, 2012 10:41:58 EST

 /*
 LANG : C++
 PROG : typo
 */

 # include <iostream>
 # include <cstring>
 # include <algorithm>
 # include <cstdio>
 # include <cstdlib>
 # include <stack>

 using namespace std;

 const int N = 1000000;

 string s;

 int l[N][3], r[N][3], len, ans, ul[N][3], ur[N][3];

 stack <int> st;

 int main () {

    freopen("typo.in", "r", stdin);
    freopen("typo.out", "w", stdout);

    cin >> s;
    len = s.size();

    for (int i = 0; i < len; ++i) {

        if(s[i] == '(') st.push(i);
        else if(st.size() > 0 && s[i] == ')') st.pop();
        else if(st.size() == 0 && s[i] == ')') {
            l[i][2] ++; ul[i][2] = 1;
        }
        l[i][1] = st.size();
        l[i][2] += (i ? l[i - 1][2] : 0);
    }

    while(!st.empty())  st.pop();
    for (int j = len - 1; j >= 0; --j) {
        if(s[j] == ')') st.push(j);
        else if(st.size() > 0 && s[j] == '(') st.pop();
        else if(st.size() == 0 && s[j] == '(') {
            r[j][2] ++; ur[j][2] = 1;
        }
        r[j][1] = st.size();
        r[j][2] += r[j + 1][2];
    }


    for (int i = 0; i < len; ++i) {

    //  cout << l[i][1] << ' ' << l[i][2] << ' ' << r[i][1] << ' ' << r[i][2] << endl;
        if(s[i] == '(') {
            int cntl = (i ? l[i - 1][1] : 0);
            int cnt2 = (i ? l[i - 1][2] : 0);
            if(cntl == r[i + 1][1] + 1 && r[i + 1][2] == 0 && cnt2 == 0)
                ans ++;

        }

        if(s[i] == ')') {
            int cnt1, cnt2;
            if(i == 0) cnt1 = 1;
            else if(ul[i][2] == 1) cnt1 = l[i][1] + 1;
            else cnt1 = l[i][1] + 2;

            if(l[i][2] != 1 && ul[i][2]) continue;
            if(l[i][2] != 0 && !ul[i][2]) continue;
            if(r[i + 1][2] != 0) continue;

            if(cnt1 == r[i + 1][1])
                ans ++;

        }

    }

    cout  << ans << endl;

 }