#include <bits/stdc++.h>
using namespace std;
using ll = long long int;
const int N = 2e5 + 5;
ll dp[N], n, match[N];
string s;
stack<pair<char, ll>> st1, st2;
int main() {
    cin >> s;
    n = (int)s.size();

    memset(match, -1, sizeof(match));

    ll inval_cnt = 0, ans = 0;
    for(int i = 0; i < n; i++) {
        char c = s[i];
        if(c == '-') {
            char cc = st2.top().first;
            int ii = st2.top().second;
            if(cc == ')' && match[ii] != -1) {
                ans -= dp[ii];
                st1.emplace('(', match[ii]);   
            } else {
                st1.pop();
            }
            st2.pop();
        } else {
            if(c == '(') st1.emplace(c, i);
            else {
                if(st1.empty() || st1.top().first == ')') {
                    st1.emplace(c, i);
                } else {
                    int l_id = st1.top().second;
                    match[i] = l_id;
                    if(l_id) dp[i] = dp[l_id - 1] + 1;
                    else dp[i] = 1;
                    ans += dp[i];
                    st1.pop();

                    // cerr << "match[" << i << "] = " << match[i] << endl;
                }
            }
            st2.emplace(c, i);
        }

        cout << ans << "\n";
    }
}