#include "beechtree.h"

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


int N, M;
vector<int> P, C;

vector<int> deg;
vector<vector<int>> graph;
vector<int> colorful;
void dfs(int u) {
  vector<int> cs;
  for (const int v : graph[u]) {
    dfs(v);
    if (!colorful[v]) {
      colorful[u] = 0;
    }
    cs.push_back(C[v]);
  }
  sort(cs.begin(), cs.end());
  for (int j = 0; j < (int)cs.size() - 1; ++j) if (cs[j] == cs[j + 1]) {
    colorful[u] = 0;
  }
}

vector<int> us;
void dfsSub(int u) {
  us.push_back(u);
  for (const int v : graph[u]) {
    dfsSub(v);
  }
}

int checkBrute(int r) {
  us.clear();
  dfsSub(r);
  const int usLen = us.size();
  sort(us.begin(), us.end());
  do {
    bool ok = true;
    vector<int> cnt(M, 0);
    for (int j = 1; j < usLen; ++j) {
      const int u = us[j];
      if (P[u] != us[cnt[C[u]]]) {
        ok = false;
        break;
      }
      ++cnt[C[u]];
    }
    if (ok) {
// cerr<<"[checkBrute r="<<r<<"] us = "<<us<<endl;
      return 1;
    }
  } while (next_permutation(us.begin() + 1, us.end()));
  return 0;
}

vector<int> ids;
int check(int r) {
  if (!colorful[r]) {
    return 0;
  }
  us.clear();
  dfsSub(r);
  const int usLen = us.size();
  sort(us.begin(), us.end(), [&](int u, int v) -> bool {
    return ((deg[u] != deg[v]) ? (deg[u] > deg[v]) : (u < v));
  });
// cerr<<"[check r="<<r<<"] us = "<<us<<endl;
  // check subset relations
  {
    vector<int> last(M, -1);
    for (int j = 0; j < usLen; ++j) {
      for (const int v : graph[us[j]]) {
        if (last[C[v]] != j - 1) {
          return 0;
        }
        last[C[v]] = j;
      }
    }
  }
  if (r != us[0]) {
    return 0;
  }
  for (int j = 1; j < usLen; ++j) {
    const int u = us[j];
    if (deg[P[u]] < deg[us[j]]) {
      return 0;
    }
  }
  deg[us[0]] = usLen;
  for (int j = 0; j < usLen; ++j) {
    ids[us[j]] = j;
  }
  vector<vector<pair<pair<int, int>, vector<int>>>> pathss(M);
  vector<int> vis(usLen, 0);
  for (int j = usLen; --j >= 1; ) if (!vis[j]) {
    int k = j;
    vector<int> ds;
    for (; ; k = ids[P[us[k]]]) {
      ds.push_back(deg[us[k]]);
      if (k == 0 || C[us[k]] != C[us[j]]) break;
      vis[k] = 1;
    }
    int sumD = 0;
    for (const int d : ds) {
      sumD += d;
    }
    pathss[C[us[j]]].emplace_back(make_pair(ds[0], sumD), ds);
  }
// cerr<<"r = "<<r<<", us = "<<us<<", pathss = "<<pathss<<endl;
  for (int c = 0; c < M; ++c) {
    auto &paths = pathss[c];
    sort(paths.begin(), paths.end());
    for (int j = 0; j < (int)paths.size() - 1; ++j) {
      const auto &ds0 = paths[j].second;
      const auto &ds1 = paths[j + 1].second;
      int lb = 0, ub = ds0.size();
      for (int x = 0; x < (int)ds1.size(); ++x) {
        auto res = equal_range(ds0.begin(), ds0.end(), ds1[x]);
        if (res.first != ds0.begin()) chmax(lb, (int)(res.first - ds0.begin()) - x);
        if (res.second != ds0.end()) chmin(ub, (int)(res.second - ds0.begin()) - x);
      }
      if (!(lb <= ub)) {
        return 0;
      }
    }
  }
  
  /*
  vector<int> cnt(M, 0);
  for (int j = 1; j < usLen; ++j) {
    const int u = us[j];
    if (P[u] != us[cnt[C[u]]]) {
      return 0;
    }
    ++cnt[C[u]];
  }
  */
  return 1;
}

vector<int> run() {
  deg.assign(N, 0);
  graph.assign(N, {});
  for (int u = 1; u < N; ++u) {
    ++deg[P[u]];
    graph[P[u]].push_back(u);
  }
  colorful.assign(N, 1);
  dfs(0);
  
  vector<int> ans(N, 0);
  ids.resize(N);
  for (int r = 0; r < N; ++r) {
    ans[r] = check(r);
  }
#ifdef LOCAL
vector<int>brt(N,0);
for(int r=0;r<N;++r)brt[r]=checkBrute(r);
if(brt!=ans){
 cerr<<"N = "<<N<<endl;
 cerr<<"M = "<<M<<endl;
 cerr<<"P = "<<P<<endl;
 cerr<<"C = "<<C<<endl;
 cerr<<"brt = "<<brt<<endl;
 cerr<<"ans = "<<ans<<endl;
}
assert(brt==ans);
#endif
  return ans;
}

std::vector<int> beechtree(int N_, int M_, std::vector<int> P_, std::vector<int> C_)
{
  N = N_;
  M = M_;
  P = P_;
  C = C_;
  for (int u = 0; u < N; ++u) {
    --C[u];
  }
  return run();
}


#ifdef LOCAL
void test(int N, const vector<int> &P) {
  for (int q = 0; q < 1 << (N - 2); ++q) {
    vector<int> C(N);
    C[0] = 0;
    C[1] = 1;
    for (int u = 2; u < N; ++u) {
      C[u] = 1 + (q >> (u - 2) & 1);
    }
    beechtree(N, 2, P, C);
  }
}
void dfsGen(int N, vector<int> &P, int u) {
  if (u == N) {
    test(N, P);
  } else {
    for (P[u] = 0; P[u] < u; ++P[u]) {
      dfsGen(N, P, u + 1);
    }
  }
}
int main() {
  for (int N = 2; ; ++N) {
    vector<int> P(N, -1);
    dfsGen(N, P, 1);
    cerr << "DONE N = " << N << endl;
  }
  return 0;
}
#endif