#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<int, ll> > lastnode;
    vector<pair<int, ll> > stk;
    ll ans = 0;
    int firstcnt = 0;
    ll firstsum = 0;
    for(int i = 0; i < s.size(); ++i) {
        char c = s[i]; 
        if(c == '-') {
            if(last.back() == '(') stk.pop_back();
            else {
                if(!lastnode.empty()) {
                    if(!stk.empty()) {
                        stk.back().second -= dp[cnt];
                        --stk.back().first;
                        ans -= stk.back().first;
                    } else {
                        firstsum -= dp[cnt];
                        --firstcnt;
                        ans -= firstcnt; 
                    }
                    stk.push_back(lastnode.back());
                    lastnode.pop_back();
                    --ans;
                    dp[cnt--] = 0; 
                }
            } 
            last.pop_back();
            cout << ans << '\n';
            continue;
        }  
        last.push_back(c);
        if(c == '(') stk.push_back(make_pair(0, 0));
        else {
            if(!stk.empty()) {
                dp[++cnt] = 1 + stk.back().second + 1ll* (stk.back().first) * (stk.back().first - 1) / 2;
                ++ans;
                lastnode.push_back(stk.back());
                stk.pop_back();             
                if(!stk.empty()) {
                    ans += stk.back().first;
                    ++stk.back().first;
                    stk.back().second += dp[cnt];
                } else {
                    ans += firstcnt;
                    ++firstcnt;
                    firstsum += dp[cnt];
                }
            }
        }
        cout << ans << '\n';
    }
}