#include <bits/stdc++.h>
using namespace std;
using ll = long long int;
using ull = unsigned long long int;
using dd = double;
using ldd = long double;
template <class T = int>
inline T readInt();
inline double readDouble();
inline int readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int getChar();
inline int peekChar();
inline bool seekEof();
inline void skipBlanks();
template <class T>
inline void writeInt(T x, char end = 0, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(double x, int len = 0);
inline void flush();
static struct buffer_flusher_t {
  ~buffer_flusher_t() { flush(); }
} buffer_flusher;
static const int buf_size = 4096;
static unsigned char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline void skipBlanks() {
  while (!isEof() && buf[buf_pos] <= 32U) buf_pos++;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline int readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-')
    s = -1, c = getChar();
  else if (c == '+')
    c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline double readDouble() {
  int s = 1, c = readChar();
  double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 1e-1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = x;
}
inline void flush() {
  if (write_buf_pos) {
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
    fflush(stdout);
  }
}
template <class T>
inline void writeInt(T x, char end, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
  if (end) writeChar(end);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  assert(x <= (1LLU << 63) - 1);
  long long t = (long long)x;
  writeInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
int _size = 1 << 20;
vector<int> tree_min(_size << 1);
vector<int> tree_max(_size << 1);
vector<int> push(_size << 1);
void PUSH(int v) {
  if (v >= _size) return;
  push[v << 1] += push[v];
  push[v << 1 | 1] += push[v];
  tree_min[v << 1] += push[v];
  tree_max[v << 1] += push[v];
  tree_min[v << 1 | 1] += push[v];
  tree_max[v << 1 | 1] += push[v];
  push[v] = 0;
}
void add(int v, int l, int r, int fl, int fr, int x) {
  if (r <= fl || fr <= l || r <= l) return;
  if (fl <= l && r <= fr) {
    push[v] += x;
    tree_max[v] += x;
    tree_min[v] += x;
    return;
  }
  PUSH(v);
  add(v << 1, l, (r + l) >> 1, fl, fr, x);
  add(v << 1 | 1, (r + l) >> 1, r, fl, fr, x);
  tree_min[v] = min(tree_min[v << 1], tree_min[v << 1 | 1]);
  tree_max[v] = max(tree_max[v << 1], tree_max[v << 1 | 1]);
}
void solve() {
  int n;
  n = readInt();
  int curr = 0;
  vector<int> is(_size);
  char k;
  int summary = 0;
  for (int i = 0; i < n; ++i) {
    k = readChar();
    if (k == 'L')
      curr = max(0, curr - 1);
    else if (k == 'R')
      ++curr;
    else if (k == '(') {
      summary -= is[curr];
      summary++;
      add(1, 0, _size, curr, _size, -is[curr]);
      add(1, 0, _size, curr, _size, 1);
      is[curr] = 1;
    } else if (k == ')') {
      summary -= is[curr];
      summary--;
      add(1, 0, _size, curr, _size, -is[curr]);
      add(1, 0, _size, curr, _size, -1);
      is[curr] = -1;
    } else {
      summary -= is[curr];
      add(1, 0, _size, curr, _size, -is[curr]);
      is[curr] = 0;
    }
    if (tree_min[1] == 0 && summary == 0) {
      writeInt(tree_max[1]);
      writeChar(' ');
    } else {
      writeInt(-1);
      writeChar(' ');
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int t;
  t = 1;
  for (int i = 0; i < t; ++i) solve();
  return 0;
}
