C. Ктулху

#include <bits/stdc++.h>

using i32 = int;
using ui32 = unsigned int;
using i64 = long long;
using ui64 = unsigned long long;


const ui32 MSIZE = 100;

std::vector<ui32> g[MSIZE];

ui32 color[MSIZE];
bool cycle[MSIZE];
bool used[MSIZE];

void UsedDfs(ui32 from) {
  used[from] = true;
  for (ui32 v : g[from]) {
    if (!used[v]) {
      UsedDfs(v);
    }
  }
}

i32 Dfs(ui32 from, ui32 parent) {
  color[from] = 1;
  for (ui32 v : g[from]) {
    if (v == parent) continue;
    if (color[v] == 1) {
      cycle[from] = true;
      return v;
    }
    if (color[v] == 0) {
      i32 result = Dfs(v, from);
      if (result >= 0) {
        cycle[from] = true;
        if (result == from) {
          return -2;
        } else {
          return result;
        }
      } else if (result == -2) {
        return -2;
      }
    }
  }
  color[from] = 2;
  return -1;
}

i32 main() {
  ui32 n, m;
  scanf("%d%d", &n, &m);
  for (ui32 i = 0; i < m; i++) {
    int f, t;
    scanf("%d%d", &f, &t);
    f--, t--;
    g[f].push_back(t);
    g[t].push_back(f);
  }

  // check that graph is connected
  UsedDfs(0);
  bool isGod = true;
  for (ui32 i = 0; i < n; i++) {
    if (!used[i]) {
      isGod = false;
    }
  }

  // check that cycle exists
  if (Dfs(0, 0) != -2) {
    isGod = false;
  }

  // check that length of cycle >= 3
  ui32 trees = 0;
  for (ui32 i = 0; i < n; i++) {
    if (cycle[i]) {
      trees++;
    }
  }
  isGod &= trees >= 3;

  // check that it is only one cycle (cycle + trees = n edges => m should be equals to n)
  isGod &= m == n;

  puts(isGod ? "FHTAGN!" : "NO");
}