DYNACON1

100 100
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conn 24 79
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rem 24 79
rem 24 79
rem 24 79
conn 24 79
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conn 79 100
rem 24 79
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100 100
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conn 24 79
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rem 24 79
rem 24 79
conn 24 79
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conn 79 100
rem 24 79
conn 79 100
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10 1000
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100 10000
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rem 53 33
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rem 14 33
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add 33 1
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rem 3 38
rem 4 53
rem 100 24
rem 41 12
rem 41 52
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rem 88 75
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rem 84 46
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rem 93 87
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rem 28 48
rem 52 19
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rem 100 95
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rem 48 9
rem 23 49
rem 50 38
rem 50 54
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rem 46 94
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rem 97 74
rem 34 11
rem 39 77
rem 51 19
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rem 97 29
conn 20 53
rem 95 7
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rem 36 50
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rem 50 40
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rem 85 92
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rem 38 91
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rem 14 44
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rem 82 30
rem 10 45
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rem 57 48
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rem 84 90
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rem 81 16
rem 10 39
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rem 34 45
rem 23 97
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rem 62 41
rem 64 38
rem 14 99
rem 90 72
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rem 53 2
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rem 86 34
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rem 72 12
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rem 90 36
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rem 84 49
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rem 14 72
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rem 7 55
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rem 26 10
rem 24 15
rem 65 13
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rem 84 41
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rem 30 21
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rem 49 6
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rem 88 40
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rem 70 44
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rem 35 57
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rem 23 34
rem 26 20
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rem 19 18
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rem 71 52
rem 52 19
rem 47 85
rem 74 62
rem 10 69
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rem 49 11
rem 10 53
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rem 61 41
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rem 48 22
rem 23 24
rem 20 41
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rem 18 44
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rem 57 28
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rem 56 9
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rem 30 57
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rem 7 98
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rem 38 33
rem 10 47
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rem 15 9
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rem 5 38
rem 51 92
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rem 64 70
rem 71 82
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rem 40 88
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rem 9 89
conn 38 17
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50 1000
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rem 11 8
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rem 25 24
rem 49 12
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rem 11 26
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rem 13 19
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rem 6 24
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rem 32 22
rem 43 37
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rem 32 22
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rem 12 4
rem 4 2
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// TODO: easy link-cut tree problem (just do links and cuts)
// http://www.spoj.com/problems/DYNACON1/
// TODO: use on an easy MST problem

#include 
using namespace std;
typedef long long ll;
#define DEBUG
#ifdef DEBUG
#define TRACE(x) cerr << #x << " = " << x << endl;
#define _ << " _ " <<
#else
#define TRACE(x) ((void)0)
#endif

const int INF = numeric_limits::max() / 2;

class Node {
 public:
  Node();
  Node(Node* _par, Node* left, Node *right, int _val);

  Node* get_root();
  void cut(Node* neighbor);
  void link(Node* child);
  Node* lca(Node* other);
  void evert(); // reroot
  int heavy_edge(Node* other);

 private:
  Node* par; // parent
  Node* c[2]; // children
  // node value and subtree accumulator value
  // accumulator function is assumed to be commutative. Otherwise, the
  // accumulator must be updated more frequently (once more after rotation, and
  // after flipping)
  int val, acc;
  bool flip; // whether children are reversed; used for evert()
  static const int default_val = -INF;

  void rot();
  void fix_c();
  void fix_par();
  void splay();
  void push_flip();
  void cut_from_par();
  void update_acc();
  Node* get_real_par();
  Node* expose();
};

Node::Node() {
  Node(nullptr, nullptr, nullptr, default_val);
}

Node::Node(Node* _par, Node* left, Node *right, int _val)
  : par(_par), c{left, right}, val(_val), flip(0) {
  fix_c();
}

Node* Node::get_real_par() {
  return par != nullptr && this != par->c[0] && this != par->c[1] ? nullptr : par;
}

void Node::fix_c() {
  for (int i = 0; i < 2; i++)
    if (c[i] != nullptr)
      c[i]->par = this;
  update_acc();
}

void Node::update_acc() {
  acc = max(val, max(c[0] == nullptr ? default_val : c[0]->val,
                     c[1] == nullptr ? default_val : c[1]->val));
}

void Node::splay() {
  Node* p, * gp;
  while ((p = get_real_par()) != nullptr) {
    gp = p->get_real_par();
    if (gp != nullptr)
      gp->push_flip();
    p->push_flip();
    push_flip();
    if (gp != nullptr)
      ((gp->c[0] == p) == (p->c[0] == this) ? p : this)->rot();
    rot();
  }
}

void Node::rot() { // rotate v towards its parent; v must have real parent
  Node* p = get_real_par();
  par = p->par;
  if (par != nullptr)
    for (int i = 0; i < 2; i++)
      if (par->c[i] == p) {
        par->c[i] = this;
        par->fix_c();
      }
  const bool rot_dir = this == p->c[0];
  p->c[!rot_dir] = c[rot_dir];
  c[rot_dir] = p;
  fix_c();
  p->fix_c();
}

// returns 1st vertex encountered that was originally in same path as root (used
// for LCA)
Node* Node::expose() {
  Node* ret = this;
  for (Node* curr = this, * pref = nullptr; curr != nullptr;
       ret = curr, pref = this, curr = par) {
    curr->splay();
    curr->c[1] = pref;
    curr->fix_c();
    splay();
  }
  return ret;
}

Node* Node::get_root() {
  expose();
  Node* root = this;
  push_flip();
  while (root->c[0] != nullptr) {
    root = root->c[0];
    root->push_flip();
  }
  root->splay();
  return root;
}

void Node::cut(Node* neighbor) {
  evert();
  assert(neighbor->par == this);
  neighbor->par = nullptr;
  for (int i = 0; i < 2; i++)
    if (c[i] == neighbor)
      c[i] = nullptr;
  fix_c();
}

void Node::link(Node* child) {
  assert(get_root() != child->get_root()); // no cycles
  child->evert();
  expose();
  child->par = this;
}

void Node::evert() {
  expose();
  flip ^= 1;
  push_flip();
}

void Node::push_flip() {
  if (flip) {
    flip = 0;
    swap(c[0], c[1]);
    for (int i = 0; i < 2; i++)
      if (c[i] != nullptr)
        c[i]->flip ^= 1;
  }
}

Node nodes[100001];

int main() {
  ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

  int n, m;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    string s;
    int u, v;
    cin >> s >> u >> v;
    switch (s[0]) {
      case 'a':
        nodes[u].link(&nodes[v]);
        break;
      case 'r':
        nodes[u].cut(&nodes[v]);
        break;
      case 'c':
        cout << (nodes[u].get_root() == nodes[v].get_root() ? "YES\n" : "NO\n");
        break;
      default:
        assert(false);
    }
  }
  return 0;
}
5 10
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add 10 5
rem 19 20
add 9 19
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rem 5 2
rem 16 10
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rem 10 9
conn 5 20
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rem 18 5
rem 19 12
rem 20 1
rem 16 7
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add 1 10
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rem 1 5
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rem 3 8
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rem 19 12
rem 2 11
conn 11 17
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rem 19 1
rem 4 14
add 2 1
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rem 7 15
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rem 17 4
rem 14 9
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rem 5 16
rem 5 9
rem 19 9
rem 15 8
rem 6 13
conn 2 8
conn 6 15
conn 3 1
rem 10 11
conn 4 11
rem 9 4
conn 17 14
rem 13 17
rem 12 4
rem 14 19
rem 5 18
rem 17 18
conn 12 7
add 4 14
rem 1 10
rem 10 15
conn 11 19
rem 8 13
conn 2 8
rem 9 20
rem 13 5
rem 12 17
rem 4 14
add 15 5
conn 16 18
rem 4 19
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add 1 11
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conn 9 7
add 3 15
rem 18 5
rem 18 6
rem 8 13
rem 17 9
conn 19 4
rem 8 9
conn 8 9
rem 2 12
conn 14 18
rem 13 15
add 1 11
rem 20 16
rem 5 2
conn 6 20
rem 4 12
rem 3 1
conn 1 2
rem 18 14
rem 5 2
rem 19 3
rem 12 20
add 18 14
conn 18 19
add 14 13
rem 7 15
add 9 5
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rem 6 16
add 15 13
rem 9 17
conn 20 10
conn 10 19
rem 5 2
add 4 11
rem 7 11
rem 12 9
rem 17 11
add 7 18
conn 15 4
conn 8 20
rem 8 6
add 5 19
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rem 4 10
rem 16 6
add 17 18
rem 7 18
rem 19 6
add 18 3
conn 5 16
conn 19 20
rem 7 19
rem 3 12
conn 14 16
conn 7 1
rem 1 20
rem 2 18
conn 11 14
rem 6 8
rem 10 6
rem 17 20
conn 13 6
rem 6 11
add 5 20
add 4 11
add 15 1
rem 5 13
conn 8 16
rem 9 13
add 11 9
rem 3 10
rem 16 10
conn 4 14
conn 5 6
rem 6 15
rem 2 10
rem 7 14
rem 3 17
add 13 1
rem 8 12
conn 14 19
add 14 4
rem 10 7
rem 8 7
conn 9 10
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conn 3 11
conn 8 9
conn 18 19
conn 6 8
rem 14 1
rem 9 16
rem 16 11
conn 1 15
conn 13 4
add 9 3
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rem 14 13
rem 11 9
rem 7 8
add 5 17
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add 4 17
conn 15 6
add 12 13
rem 1 12
rem 6 18
conn 4 1
rem 5 1
rem 11 10
rem 3 19
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rem 13 16
rem 7 17
rem 4 11
add 5 9
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conn 9 16
conn 1 10
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rem 6 11
rem 17 12
rem 3 20
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rem 20 8
add 2 15
rem 18 16
rem 18 1
conn 10 17
conn 10 16
rem 11 6
conn 5 7
rem 20 5
conn 9 17
rem 3 12
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rem 5 10
rem 6 2
rem 7 12
add 2 10
rem 13 14
rem 10 7
rem 1 10
conn 15 4
rem 20 11
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rem 10 9
rem 20 7
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rem 6 11
rem 2 6
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conn 10 8
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rem 14 4
rem 8 18
rem 11 1
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rem 2 4
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rem 17 19
rem 9 5
rem 6 12
conn 16 4
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rem 7 19
rem 1 8
conn 17 20
rem 15 5
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rem 6 9
add 18 4
rem 2 10
rem 3 20
rem 13 5
rem 16 13
conn 4 20
conn 12 19
rem 20 6
conn 15 8
conn 11 19
rem 6 5
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rem 20 18
rem 5 16
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rem 14 13
rem 17 7
conn 20 9
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rem 15 17
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rem 15 10
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rem 12 11
rem 6 3
conn 2 18
conn 8 19
rem 5 14
rem 8 18
add 7 5
rem 16 7
add 1 8
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conn 17 18
rem 8 12
rem 14 12
add 1 19
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rem 4 15
rem 15 2
rem 3 14
rem 9 8
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rem 14 7
add 11 13
conn 9 13
rem 13 18
rem 3 20
rem 17 6
rem 8 13
rem 17 12
rem 1 10
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rem 18 10
rem 1 16
rem 5 18
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rem 10 9
add 18 2
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conn 1 2
rem 16 18
rem 18 15
conn 4 6
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conn 15 4
rem 17 15
rem 3 10
rem 12 13
rem 19 6
rem 10 2
rem 17 2
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add 1 6
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rem 12 19
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conn 8 12
rem 1 7
rem 16 15
rem 2 1
conn 17 13
rem 8 18
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rem 10 2
rem 18 6
rem 16 11
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rem 2 11
add 9 7
conn 10 18
rem 10 15
conn 20 16
conn 3 12
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rem 13 12
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add 3 10
rem 9 18
rem 5 4
add 20 7
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rem 13 3
rem 13 4
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conn 12 3
rem 3 8
rem 11 9
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rem 1 11
rem 3 12
conn 19 2
rem 17 7
add 13 19
rem 17 14
rem 16 14
conn 14 6
conn 13 11
rem 19 16
rem 3 5
rem 14 20
rem 20 13
rem 10 5
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rem 3 17
rem 18 4
conn 9 10
add 18 19
rem 3 4
rem 3 17
add 14 15
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add 11 15
rem 12 6
rem 14 8
rem 6 9
conn 12 18
rem 11 16
conn 5 15
conn 12 4
rem 8 1
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rem 14 12
rem 18 9
rem 2 15
add 16 5
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conn 1 4
rem 2 11
rem 15 14
conn 18 13
rem 19 10
10 40
rem 6 5
add 7 10
conn 4 1
rem 5 7
conn 3 4
rem 5 6
conn 2 3
add 1 8
conn 1 8
rem 4 1
rem 10 8
conn 2 1
rem 10 6
rem 9 8
conn 1 7
rem 2 1
add 7 1
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rem 2 8
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conn 5 8
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rem 7 3
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add 8 6
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conn 8 6
rem 9 5
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rem 9 7
conn 7 1
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conn 6 10
5 12
add 3 4
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rem 4 3
conn 5 4
add 2 3
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rem 1 2
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rem 0 4
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rem 0 3
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rem 0 2
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rem 0 4
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rem 4 0
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rem 2 1
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rem 3 0
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rem 4 2
add 1 2
rem 1 3
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rem 2 1
conn 4 3
5 46
add 2 3
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rem 1 4
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rem 3 4
rem 1 2
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rem 0 1
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rem 4 2
rem 0 4
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rem 1 3
rem 0 3
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rem 0 1
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rem 0 2
add 2 0
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rem 2 4
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rem 4 3
rem 0 4
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rem 4 0
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rem 3 0
rem 2 1
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rem 3 0
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rem 4 2
add 1 2
rem 1 3
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rem 2 1
conn 4 3
5 46
add 3 4
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rem 2 5
add 1 2
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rem 4 5
rem 2 3
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rem 1 2
add 4 5
rem 5 3
rem 1 5
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rem 2 5
rem 2 4
rem 1 4
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rem 1 2
add 5 2
rem 1 3
add 3 1
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rem 3 5
add 5 1
rem 5 4
rem 1 5
add 4 5
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rem 5 1
add 1 2
rem 4 1
rem 3 2
add 2 4
rem 4 1
add 5 4
add 4 3
rem 5 3
add 2 3
rem 2 4
add 5 4
rem 3 2
conn 5 4