#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cstring>
#define p 1000000007
#define N 300005
#define ll long long
using namespace std;

struct oper{
    char type;
    int lst;
    inline oper(char _type=0,int _lst=0):type(_type),lst(_lst){}
};

oper stk2[N];
char str[N];
int stk[N];
int n,top = 100000,lef,top2;
ll ans;

int main(){
    scanf("%s",str);
    n = strlen(str);
    for(int i=0;i<n;++i){
        if(str[i]=='('){
            stk[++top] = 0;
            ++lef;
            stk2[++top2] = oper('(',0);
        }else if(str[i]==')'){
            if(lef==0){
                stk2[++top2] = oper(')',stk[top]);
                stk[top] = 0;
            }else{
                top--;
                ans += ++stk[top];
                --lef;
                stk2[++top2] = oper(')',0);
            }
        }else{
            oper op = stk2[top2--];
            if(op.type=='(') top--,lef--;
            else{
                if(op.lst!=0) stk[top] = op.lst;
                else{
                    ++lef;
                    ans -= stk[top]--;
                    top++;
                }
            }
        }
        printf("%lld\n",ans);
    }
}