#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
#define rep(i,a,b) for(int i = a; i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define PB push_back
#define FS first
#define SD second
#define ary(k) array<int,k>
template<class A, class B> void cmx(A& x, B y){ x = max<A>(x,y); }
template<class A, class B> void cmn(A& x, B y){ x = min<A>(x,y); }
typedef pair<int,int> pii;
typedef vector<int> vi;


signed main(){
	cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit);
	string s; cin >> s;
	vi psa = {0};
	vi ours;
	vi prv = {-1};
	map<int,vi> pos;
	pos[0].PB(0);
	int ptr = 0;
		

	int cum = 0;
	auto add = [&](int x){
		ptr++;
		// psa[n]-psa[l] = 0
		psa.PB(psa.back()+x);
		pos[psa.back()].PB(ptr);
		// psa[n] < psa[l-1]	
		int our_prv = -1;
		if(x < 0){
			our_prv = ptr-1;
		} else{
			int tmp = prv.back();
			if(tmp != -1) our_prv = prv[tmp];
		}
		int cnt = pos[psa.back()].end() - lower_bound(all(pos[psa.back()]),our_prv+1);
		cnt--; // ourselves
		ours.PB(cnt);	
		//cerr << ptr << " " << our_prv << " " << x << " " << psa.back() << " " << cnt << "\n";
		prv.PB(our_prv);
		cum += cnt;
	};
	auto pop = [&](){
		cum -= ours.back();
		int v = psa.back();
		psa.pop_back();
		prv.pop_back();
		pos[v].pop_back();
		ours.pop_back();
		ptr--;
	};
	for(char c : s){
		if(c == '-') pop();
		else add(c == '(' ? -1 : 1);
		cout << cum << "\n";
	}
}