#include <bits/stdc++.h>

using ll = long long;
using ld = long double;

using namespace std;

int N = 0;

struct node {
    int lb, rb;
    int lazy = 0, a = 0;
    node *l = 0, *r = 0;
    pair<int, int> maxim, minim;

    node(int _lb, int _rb) {
        lb = _lb; rb = _rb;
        if (lb + 1 < rb) {
            int t = (lb + rb) / 2;
            l = new node(lb, t);
            r = new node(t, rb);
        }
        maxim = { lb, 0 };
        minim = { lb, 0 };
    }

    void add(int x, int _l, int _r) {
        if (_r < lb || _l >= rb)
            return;

        if (_l <= lb && rb - 1 <=_r)
            lazy += x;
        else {
            l->add(x, _l, _r); r->add(x, _l, _r);
            auto a = l->maxim, b = r->maxim;
            a.second += l->lazy;
            b.second += r->lazy;
            if (a.second < b.second)
                swap(a, b);
            maxim = a;

            a = l->minim, b = r->minim;
            a.second += l->lazy;
            b.second += r->lazy;
            if (a.second > b.second)
                swap(a, b);
            minim = a;
        }
    }

    void push() {
        maxim.second += lazy;
        minim.second += lazy;
        if (lb + 1 == rb) {
            lazy = 0;
            return;
        }
        l->lazy += lazy; r->lazy += lazy;
        lazy = 0;
    }

    pair<int, int> max(int _l, int _r) {
        push();

        if (_r < lb || _l >= rb)
            return{ -1, -1 };

        if (_l <= lb && _r >= rb - 1)
            return maxim;
        else {
            auto a = l->max(_l, _r), b = r->max(_l, _r);
            if (a.second < b.second)
                swap(a, b);
            return a;
        }
    }
    pair<int, int> min(int _l, int _r) {
        push();

        if (_r < lb || _l >= rb)
            return{ -1, -1 };

        if (_l <= lb && _r >= rb - 1)
            return minim;
        else {
            auto a = l->min(_l, _r), b = r->min(_l, _r);
            if (a.second > b.second)
                swap(a, b);
            return a;
        }
    }
};

int main() {
    ios::sync_with_stdio(0);

    int n; cin >> n;
    vector<char> a(n);
    int it = 0;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        if (a[i] == 'R')
            it++;
        else if (a[i] == 'L')
            it--;
        else
            N = max(N, it);
    }
    N++;
    node *d = new node(0, N);

    vector<char> arr(N);
    it = 0;
    int bal = 0;
    for (int i = 0; i < n; i++) {
        if (a[i] == 'L')
            it--;
        else if (a[i] == 'R')
            it++;
        else if (a[i] == '(') {
            if (a[i] == arr[it])
                continue;
            if (arr[it] == ')') {
                d->add(2, it, N - 1);
                bal += 2;
            }
            else {
                d->add(1, it, N - 1);
                bal++;
            }
            arr[it] = '(';
        }
        else if (a[i] == ')') {
            if (a[i] == arr[it])
                continue;
            if (arr[it] == '(') {
                d->add(-2, it, N - 1);
                bal -= 2;
            }
            else {
                d->add(-1, it, N - 1);
                bal--;
            }
            arr[it] = ')';
        }
        else {
            if (arr[it] == '(') {
                bal--;
                d->add(-1, it,  N - 1);
            }
            else if (arr[it] == ')') {
                bal++;
                d->add(1, it, N - 1);
            }
            arr[it] = 'a';
        }

        if (bal != 0 || d->min(0, N - 1).second)
            cout << -1;
        else
            cout << d->max(0, N - 1).second;
        cout << " ";
    }
    return 0;
}