#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
 
using namespace std;
using namespace __gnu_pbds;
typedef long long int lld;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
#define rep(i,a,b) for(int i=a;i<b;i++)
#define trav(a,v) for(auto a:v)
const int MAX=1'000'000;
vector<int> idx[MAX];

void solve(){
	string s;
	cin>>s;
	int sum=s.size()+5;
	int cnt=0;
	idx[sum].push_back(cnt);
	cnt++;
	lld tot=0;
	stack<char> st;
	trav(a,s){
		if(a=='('){
			st.push(a);
			sum++;
			
			cnt++;
			int top=-1;
			if(idx[sum-1].size()>0){
				top=idx[sum-1][idx[sum-1].size()-1];
			}
			tot+=idx[sum].end()-lower_bound(idx[sum].begin(),idx[sum].end(),top);
			idx[sum].push_back(cnt);
		}else{
			if(a==')'){
				st.push(a);
				sum--;
				
				cnt++;
				int top=-1;
				if(idx[sum-1].size()>0){
					top=idx[sum-1][idx[sum-1].size()-1];
				}
				tot+=idx[sum].end()-lower_bound(idx[sum].begin(),idx[sum].end(),top);
				idx[sum].push_back(cnt);
			}else{
				idx[sum].pop_back();
				cnt--;
				int top=-1;
				if(idx[sum-1].size()>0){
					top=idx[sum-1][idx[sum-1].size()-1];
				}
				tot-=idx[sum].end()-lower_bound(idx[sum].begin(),idx[sum].end(),top);
				if(st.top()=='(')sum--;
				else sum++;
				st.pop();
			}
		}
		cout<<tot<<"\n";
	}
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int tt=1;
	//cin>>tt;
	while(tt--){
		solve();
	}
}