#include <bits/stdc++.h>
using namespace std;
struct dsu {
  vector<int> id;
  dsu(int n) { id = vector<int>(n, -1); }
  inline int par(int a) const { return id[a] >= 0 ? id[a] : a; }
  int find(int a) {
    while (id[a] >= 0) {
      id[a] = par(par(a));
      a = id[a];
    }
    return a;
  }
  bool unite(int a, int b) {
    a = find(a);
    b = find(b);
    if (a == b) return false;
    if (id[a] > id[b]) {
      swap(a, b);
    }
    id[a] += id[b];
    id[b] = a;
    return true;
  }
};
struct tr {
  long long a, b;
  int t;
};
bool intersect(long long a, long long b, long long c, long long d) {
  return b >= c && d >= a;
}
vector<pair<long long, long long>> vertices;
vector<pair<int, int>> edges;
vector<tr> blocks;
int add(long long from, long long to) {
  vertices.emplace_back(from, to);
  return (int)vertices.size() - 1;
}
pair<int, int> boo(int depth, int idL, int idR, long long from, long long to) {
  if (idL > idR) {
    int id = add(from, to);
    return {id, id};
  } else if (idL == idR) {
    const tr &in = blocks[idL];
    if (in.a <= from && to <= in.b) {
      int id = add(from, to);
      return {id, id};
    } else if (!intersect(from, to, in.a, in.b)) {
      int id = add(from, to);
      return {id, id};
    }
  }
  long long mid = (from + to) / 2;
  vector<int> left, right;
  int leftId = idL - 1;
  int rightId = idR + 1;
  for (int id = idL; id <= idR; id++) {
    const tr &bl = blocks[id];
    if (intersect(bl.a, bl.b, from, mid)) {
      leftId = id;
    }
    if (intersect(bl.a, bl.b, mid + 1, to)) {
      if (rightId == idR + 1) {
        rightId = id;
      }
    }
  }
  const pair<int, int> lv = boo(depth - 1, idL, leftId, from, mid);
  const pair<int, int> rv = boo(depth - 1, rightId, idR, mid + 1, to);
  int pl = lv.first, pr = rv.first;
  while (pl <= lv.second && pr <= rv.second) {
    long long rL = vertices[pr].first ^ (1LL << depth);
    long long rR = vertices[pr].second ^ (1LL << depth);
    if (intersect(rL, rR, vertices[pl].first, vertices[pl].second)) {
      edges.emplace_back(pl, pr);
    }
    if (vertices[pl].second <= rR) {
      pl++;
    } else {
      pr++;
    }
  }
  return make_pair(lv.first, rv.second);
}
void foo() {
  int n, m;
  cin >> n >> m;
  vector<tr> queries;
  blocks.clear();
  for (int time = 0; time < m; time++) {
    string type;
    cin >> type;
    long long x, y;
    cin >> x >> y;
    if (type == "ask") {
      queries.push_back({x, y, time});
    } else {
      blocks.push_back({x, y, time});
    }
  }
  vertices.clear();
  edges.clear();
  sort(blocks.begin(), blocks.end(),
       [&](const tr &b1, const tr &b2) { return b1.a < b2.a; });
  boo(n - 1, 0, (int)blocks.size() - 1, 0, (1LL << n) - 1);
  const int N = vertices.size();
  const int M = edges.size();
  vector<vector<int>> time_edge(m + 1);
  vector<int> time_ver(N, m);
  int ptr = 0;
  for (int i = 0; i < N; i++) {
    while (ptr < (int)blocks.size() && blocks[ptr].b < vertices[i].first) {
      ptr++;
    }
    if (ptr == (int)blocks.size()) {
      break;
    }
    if (blocks[ptr].a <= vertices[i].first &&
        vertices[i].first <= blocks[ptr].b) {
      time_ver[i] = blocks[ptr].t;
    }
  }
  for (int i = 0; i < M; i++) {
    int tm = min(time_ver[edges[i].first], time_ver[edges[i].second]);
    time_edge[tm].push_back(i);
  }
  auto get_ver = [&](long long x) -> int {
    int lo = 0, hi = N - 1;
    while (1) {
      int mid = lo + (hi - lo) / 2;
      const auto &v = vertices[mid];
      if (x < v.first) {
        hi = mid - 1;
      } else if (v.second < x) {
        lo = mid + 1;
      } else {
        return mid;
      }
    }
  };
  dsu g(N);
  const int Q = queries.size();
  vector<int> ans(Q, -1);
  int pq = Q - 1;
  for (int t = m; pq >= 0; t--) {
    auto &q = queries[pq];
    if (q.t == t) {
      int va = get_ver(q.a);
      int vb = get_ver(q.b);
      ans[pq] = (g.find(va) == g.find(vb));
      pq--;
    } else {
      for (int id : time_edge[t]) {
        g.unite(edges[id].first, edges[id].second);
      }
    }
  }
  for (int x : ans) {
    cout << x << '\n';
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  foo();
}

### Prompt

Construct a cpp code solution to the problem outlined:

<image>

As mentioned previously William really likes playing video games. In one of his favorite games, the player character is in a universe where every planet is designated by a binary number from 0 to 2^n - 1. On each planet, there are gates that allow the player to move from planet i to planet j if the binary representations of i and j differ in exactly one bit.

William wants to test you and see how you can handle processing the following queries in this game universe:

  * Destroy planets with numbers from l to r inclusively. These planets cannot be moved to anymore.
  * Figure out if it is possible to reach planet b from planet a using some number of planetary gates. It is guaranteed that the planets a and b are not destroyed. 

Input

The first line contains two integers n, m (1 ≤ n ≤ 50, 1 ≤ m ≤ 5 ⋅ 10^4), which are the number of bits in binary representation of each planets' designation and the number of queries, respectively.

Each of the next m lines contains a query of two types:

block l r — query for destruction of planets with numbers from l to r inclusively (0 ≤ l ≤ r < 2^n). It's guaranteed that no planet will be destroyed twice.

ask a b — query for reachability between planets a and b (0 ≤ a, b < 2^n). It's guaranteed that planets a and b hasn't been destroyed yet.

Output

For each query of type ask you must output "1" in a new line, if it is possible to reach planet b from planet a and "0" otherwise (without quotation marks).

Examples

Input


3 3
ask 0 7
block 3 6
ask 0 7


Output


1
0


Input


6 10
block 12 26
ask 44 63
block 32 46
ask 1 54
block 27 30
ask 10 31
ask 11 31
ask 49 31
block 31 31
ask 2 51


Output


1
1
0
0
1
0

Note

The first example test can be visualized in the following way:

<image>

Response to a query ask 0 7 is positive.

Next after query block 3 6 the graph will look the following way (destroyed vertices are highlighted):

<image>

Response to a query ask 0 7 is negative, since any path from vertex 0 to vertex 7 must go through one of the destroyed vertices.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct dsu {
  vector<int> id;
  dsu(int n) { id = vector<int>(n, -1); }
  inline int par(int a) const { return id[a] >= 0 ? id[a] : a; }
  int find(int a) {
    while (id[a] >= 0) {
      id[a] = par(par(a));
      a = id[a];
    }
    return a;
  }
  bool unite(int a, int b) {
    a = find(a);
    b = find(b);
    if (a == b) return false;
    if (id[a] > id[b]) {
      swap(a, b);
    }
    id[a] += id[b];
    id[b] = a;
    return true;
  }
};
struct tr {
  long long a, b;
  int t;
};
bool intersect(long long a, long long b, long long c, long long d) {
  return b >= c && d >= a;
}
vector<pair<long long, long long>> vertices;
vector<pair<int, int>> edges;
vector<tr> blocks;
int add(long long from, long long to) {
  vertices.emplace_back(from, to);
  return (int)vertices.size() - 1;
}
pair<int, int> boo(int depth, int idL, int idR, long long from, long long to) {
  if (idL > idR) {
    int id = add(from, to);
    return {id, id};
  } else if (idL == idR) {
    const tr &in = blocks[idL];
    if (in.a <= from && to <= in.b) {
      int id = add(from, to);
      return {id, id};
    } else if (!intersect(from, to, in.a, in.b)) {
      int id = add(from, to);
      return {id, id};
    }
  }
  long long mid = (from + to) / 2;
  vector<int> left, right;
  int leftId = idL - 1;
  int rightId = idR + 1;
  for (int id = idL; id <= idR; id++) {
    const tr &bl = blocks[id];
    if (intersect(bl.a, bl.b, from, mid)) {
      leftId = id;
    }
    if (intersect(bl.a, bl.b, mid + 1, to)) {
      if (rightId == idR + 1) {
        rightId = id;
      }
    }
  }
  const pair<int, int> lv = boo(depth - 1, idL, leftId, from, mid);
  const pair<int, int> rv = boo(depth - 1, rightId, idR, mid + 1, to);
  int pl = lv.first, pr = rv.first;
  while (pl <= lv.second && pr <= rv.second) {
    long long rL = vertices[pr].first ^ (1LL << depth);
    long long rR = vertices[pr].second ^ (1LL << depth);
    if (intersect(rL, rR, vertices[pl].first, vertices[pl].second)) {
      edges.emplace_back(pl, pr);
    }
    if (vertices[pl].second <= rR) {
      pl++;
    } else {
      pr++;
    }
  }
  return make_pair(lv.first, rv.second);
}
void foo() {
  int n, m;
  cin >> n >> m;
  vector<tr> queries;
  blocks.clear();
  for (int time = 0; time < m; time++) {
    string type;
    cin >> type;
    long long x, y;
    cin >> x >> y;
    if (type == "ask") {
      queries.push_back({x, y, time});
    } else {
      blocks.push_back({x, y, time});
    }
  }
  vertices.clear();
  edges.clear();
  sort(blocks.begin(), blocks.end(),
       [&](const tr &b1, const tr &b2) { return b1.a < b2.a; });
  boo(n - 1, 0, (int)blocks.size() - 1, 0, (1LL << n) - 1);
  const int N = vertices.size();
  const int M = edges.size();
  vector<vector<int>> time_edge(m + 1);
  vector<int> time_ver(N, m);
  int ptr = 0;
  for (int i = 0; i < N; i++) {
    while (ptr < (int)blocks.size() && blocks[ptr].b < vertices[i].first) {
      ptr++;
    }
    if (ptr == (int)blocks.size()) {
      break;
    }
    if (blocks[ptr].a <= vertices[i].first &&
        vertices[i].first <= blocks[ptr].b) {
      time_ver[i] = blocks[ptr].t;
    }
  }
  for (int i = 0; i < M; i++) {
    int tm = min(time_ver[edges[i].first], time_ver[edges[i].second]);
    time_edge[tm].push_back(i);
  }
  auto get_ver = [&](long long x) -> int {
    int lo = 0, hi = N - 1;
    while (1) {
      int mid = lo + (hi - lo) / 2;
      const auto &v = vertices[mid];
      if (x < v.first) {
        hi = mid - 1;
      } else if (v.second < x) {
        lo = mid + 1;
      } else {
        return mid;
      }
    }
  };
  dsu g(N);
  const int Q = queries.size();
  vector<int> ans(Q, -1);
  int pq = Q - 1;
  for (int t = m; pq >= 0; t--) {
    auto &q = queries[pq];
    if (q.t == t) {
      int va = get_ver(q.a);
      int vb = get_ver(q.b);
      ans[pq] = (g.find(va) == g.find(vb));
      pq--;
    } else {
      for (int id : time_edge[t]) {
        g.unite(edges[id].first, edges[id].second);
      }
    }
  }
  for (int x : ans) {
    cout << x << '\n';
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  foo();
}

```