#include <bits/stdc++.h>
using namespace std;

#ifdef genshin
#include <experimental/iterator>
#endif
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using uint = unsigned int;
const double EPS = 1e-8;
const int INF = 0x3F3F3F3F;
const ll LINF = 46 * ll(1e17);
const int MOD = 1e9 + 7;
const int maxn = 2e5 + 25;
ll dp[maxn];
signed main() { ios::sync_with_stdio(0); cin.tie(0);
    string s;
    cin >> s;
    int cnt = 0;
    vector<char> last;
    vector<pair<char, pair<int, ll> > > lastnode;
    vector<pair<char, pair<int, ll> > > stk;
    stk.push_back(make_pair(')', make_pair(0, 0)));
    ll ans = 0;
    for(int i = 0; i < s.size(); ++i) {
        char c = s[i]; 
        if(c == '-') {
            if(last.back() == 0) stk.pop_back();
            else if(last.back() == 1) {
                stk.back().second.second -= dp[cnt];
                --stk.back().second.first;
                ans -= stk.back().second.first;
                stk.push_back(lastnode.back());
                lastnode.pop_back();
                --ans;
                dp[cnt--] = 0; 
            } else stk.pop_back(); 
            last.pop_back();
            cout << ans << '\n';
            continue;
        }  
        if(c == '(') {
            stk.push_back(make_pair(c, make_pair(0, 0)));
            last.push_back(0);
        } else {
            if(stk.back().first == '(') {
                dp[++cnt] = 1 + stk.back().second.second + 1ll* (stk.back().second.first) * (stk.back().second.first - 1) / 2;
                ++ans;
                lastnode.push_back(stk.back());
                stk.pop_back();             
                ans += stk.back().second.first;
                ++stk.back().second.first;
                stk.back().second.second += dp[cnt];
                last.push_back(1);
            } else {
                stk.push_back(make_pair(c, make_pair(0, 0)));
                last.push_back(2);
            }
        }
        cout << ans << '\n';
    }
}