Problem p02573 (C++)

Buggy submission (status: Time Limit Exceeded):
using namespace std;

#include <bits/stdc++.h>

typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;

typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<db, db> pd;

typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;

typedef set<int> si;
typedef set<ll> sl;
typedef map<int, int> mii;

#define mp make_pair
#define sz(x) (int)x.size()
#define len(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
// #define pf push_front
// #define pb push_back
#define eb emplace_back
#define ep emplace
#define lb lower_bound
#define ub upper_bound

#define vfor(i, a, b) for (int i = (a); i < (b); ++i)
#define f0r(i, a) vfor(i, 0, a)
#define rof(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define r0f(i, a) rof(i, 0, a)
#define trav(a, x) for (auto &a : x)
#define def(fname, rtype, args, ...)                                           \
  function<rtype args> fname = [__VA_ARGS__] args

#define boost() cin.tie(0), cin.sync_with_stdio(0)

template <class T>
void binstf(T &found, T a, T b, function<bool(T)> test, bool TF = true) {
  T i = a, j = b;
  bool da = test(a), db = test(b);
  if ((da != TF) or (db == TF)) {
    cerr << "---[BS: TF = " << TF << "]---" << endl;
    cerr << a << "->" << da << endl;
    cerr << b << "->" << db << endl;
  }
  while (j - i > 1) {
    T m = (i + j) / 2;
    if (test(m) == TF)
      i = m;
    else
      j = m;
  }
  found = i;
  if (not TF)
    found++;
}

#define binsft(a, b, c, d) binstf(a, b, c, d, false);

template <class T> T dpow(T a, T power) {
  T result = 1;
  while (power) {
    if (power % 2)
      result *= a;
    power /= 2, a = a * a;
  }
  return result;
}

const ld PI = acos((ld)-1);
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());

template <class T> bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }

template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

template <class T> bool reorder(T &a, T &b) {
  return (a > b) ? swap(a, b), 1 : 0;
}

// INPUT
template <class A> void re(complex<A> &c);

template <class A, class B> void re(pair<A, B> &p);

template <class A> void re(vector<A> &v);

template <class A, size_t SZ> void re(array<A, SZ> &a);

#define ore(type, x)                                                           \
  type x;                                                                      \
  re(x);
#define ire(x) ore(int, x);
#define vire(x) ore(vi, x);
#define lre(x) ore(ll, x);

template <class T> void re(T &x) { cin >> x; }

void re(db &d) {
  str t;
  re(t);
  d = stod(t);
}

void re(ld &d) {
  str t;
  re(t);
  d = stold(t);
}

template <class H, class... T> void re(H &h, T &...t) {
  re(h);
  re(t...);
}

template <class A> void re(complex<A> &c) {
  A a, b;
  re(a, b);
  c = {a, b};
}

template <class A, class B> void re(pair<A, B> &p) { re(p.first, p.second); }

template <class A> void re(vector<A> &x) { trav(a, x) re(a); }

template <class A, size_t SZ> void re(array<A, SZ> &x) { trav(a, x) re(a); }

template <class T> T gcd(T a, T b) {
  a = a < 0 ? -a : a;
  b = b < 0 ? -b : b;
  if (a * b == 0)
    return max(a, b);
  else
    return gcd(min(a, b), max(a, b) % min(a, b));
}

const int MODE107 = 1000000007;

template <class T> T modop(T a, T mode = MODE107) {
  a = a % mode;
  if (a < 0)
    a += mode;
  return a;
}

template <class T> T inv(T a, T mode = MODE107) {
  T coefa = 1, coefb = 0;
  T aa = a, bb = mode;
  while (aa != 1) {
    if (aa > bb)
      swap(coefa, coefb), swap(aa, bb);
    T cc = bb / aa;
    bb -= cc * aa, coefb -= cc * coefa;
    swap(coefa, coefb), swap(aa, bb);
  }
  return coefa;
}

const int uplrDX[] = {-1, 1, 0, 0};
const int uplrDY[] = {0, 0, -1, 1};

#define ts to_string

str ts(char c) { return str(1, c); }

str ts(bool b) { return b ? "true" : "false"; }

str ts(const char *s) { return (str)s; }

str ts(str s) { return s; }

template <class A> str ts(complex<A> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}

str ts(vector<bool> v) {
  str res = "{";
  f0r(i, sz(v)) res += char('0' + v[i]);
  res += "}";
  return res;
}

template <size_t SZ> str ts(bitset<SZ> b) {
  str res = "";
  f0r(i, SZ) res += char('0' + b[i]);
  return res;
}

template <class A, class B> str ts(pair<A, B> p);

template <class T> str ts(T v) { // containers with begin(), end()
  bool fst = 1;
  str res = "{";
  for (const auto &x : v) {
    if (!fst)
      res += ", ";
    fst = 0;
    res += ts(x);
  }
  res += "}";
  return res;
}

template <class A, class B> str ts(pair<A, B> p) {
  return "(" + ts(p.first) + ", " + ts(p.second) + ")";
}

// OUTPUT
template <class A> void pr(A x) { cout << ts(x); }

template <class H, class... T> void pr(const H &h, const T &...t) {
  pr(h);
  pr(t...);
}

void ps() { pr("\n"); } // print w/ spaces
template <class H, class... T> void ps(const H &h, const T &...t) {
  pr(h);
  if (sizeof...(t))
    pr(" ");
  ps(t...);
}

// DEBUG
void DBG() { cerr << "]" << endl; }

template <class H, class... T> void DBG(H h, T... t) {
  cerr << ts(h);
  if (sizeof...(t))
    cerr << ", ";
  DBG(t...);
}

#ifdef LOCAL // compile with -DLOCAL
#define dbg(...)                                                               \
  cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",           \
      DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif

// REINITIALIZE ARRAYS BETWEEN TCs

/**
 * Description: Use in place of \texttt{complex<T>}.
 * Source: http://codeforces.com/blog/entry/22175, KACTL
 * Verification: various
 */

typedef int T;

int sgn(T a) { return (a > 0) - (a < 0); }

T sq(T a) { return a * a; }

// using namespace Point;

typedef unsigned long long ull;

class trie {
public:
  map<char, trie> l;

  void add(string t) {
    if (t.length() > 0) {
      l[t[0]].add(t.substr(1));
    }
  }

  bool contains(string t) {
    if (not l.count(t[0]))
      return false;
    return l[t[0]].contains(t.substr(1));
  }
};

template <class T> class rq {
  /* range query
   */
  vector<vector<T>> content;
  function<T(T, T)> op;

public:
  rq(vector<T> &orig, function<T(T, T)> operation) {
    op = operation;
    int size = 1;
    content.emplace_back(orig);
    while (size < orig.size()) {
      size *= 2;
      content.emplace_back(0);
      auto &todo = content.back(), &from = content[content.size() - 2];
      f0r(i, sz(from) - size / 2) {
        todo.eb(op(from[i],
                   from[i + size / 2])); //[i ~ i+s[ = [i, i+s/2[ + [i+s/2,i+s[
      }
    }
  }

  T query(int i, int j) { //[i,j[
    if (j <= i or j > content[0].size() or i < 0 or i >= content[0].size()) {
      cerr << "i=" << i << endl;
      cerr << "j=" << j << endl;
      throw "bad i j";
    }
    tie(i, j) = mp(min(i, j), max(i, j));
    int size = 1, pow = 0;
    while (size * 2 < j - i) {
      size *= 2, pow++;
    }
    assert(pow < content.size());
    auto &c = content[pow];
    assert(i < c.size() and i >= 0);
    assert(j - size < c.size() and j - size >= 0);
    T dbg = op(content[pow][i], content[pow][j - size]);
    return dbg;
  }
};

template <class T> class maxflow {
public:
  typedef T unit;
  int src, drn; // source and drain node id
  vector<vi> adj, radj;
  map<pi, unit> lims;
  map<pi, unit> rlims; // will contain solution after solve()
  void genradj() {
    radj.resize(sz(adj));
    f0r(from, sz(adj)) {
      trav(to, adj[from]) { radj[to].emplace_back(from); }
    }
  }

  unit solve() {
    while (true) {
      map<int, pair<pi, unit>> backtrack;
      bool found = false;
      set<int> seen; // bfs from src
      queue<pair<int, unit>> todo;
      todo.emplace(src, -1);
      while (not todo.empty()) {
        int from = todo.front().first;
        unit bottleneck = todo.front().second;
        todo.pop();
        if (from == drn) {
          found = true;
          break;
        }
        trav(to, adj[from]) {
          pi edge = mp(from, to);
          unit bn = min(bottleneck, lims[edge]);
          if (bn and not seen.count(to)) {
            seen.emplace(to);
            todo.emplace(to, bn);
            backtrack[to] = mp(edge, bn);
          }
        }

        trav(to, radj[from]) {
          pi edge = mp(to, from);
          unit bn = min(bottleneck, rlims[edge]);
          if (bn and not seen.count(to)) {
            seen.emplace(to);
            todo.emplace(to, bn);
            backtrack[to] = mp(edge, bn);
          }
        }
      }
      if (not found)
        break;
      else {
        list<pi> edges;
        int to = drn;
        unit flow = backtrack[to].second;
        while (to != src) {
          pi edge = backtrack[to].first;
          int from = edge.first + edge.second - to;
          edges.emplace_front(edge);
          to = from;
        }
        int from = src;
        trav(e, edges) {
          if (e.first == from)
            rlims[e] += flow, lims[e] -= flow;
          else
            rlims[e] -= flow, lims[e] += flow;
          from = e.first + e.second - from;
        }
      }
    }
    unit res = 0;
    trav(to, adj[src]) res += rlims[mp(src, to)];
    return res;
  }
};

template <class T> class SuffArr {
public:
  vector<vi> pow2ranks;
  int loop;
  int n;

  SuffArr() {}

  SuffArr(vector<T> &in, int loop_) { reset(in, loop_); }

  SuffArr(string &in, int loop_) {
    vector<T> cached;
    trav(c, in) cached.emplace_back(c);
    reset(cached, loop_);
  }

  void reset(string &in, int loop_) {
    vector<T> cached;
    trav(c, in) cached.emplace_back(c);
    reset(cached, loop_);
  }

  void reset(vector<T> &in, int loop_) { // N chars in charspace K
    loop = loop_, n = in.size();
    pow2ranks.clear();
    {
      vector<pair<T, int>> initial;
      map<T, queue<int>> shelf;
      f0r(i, n) shelf[in[i]].emplace(i); // logK per write, NlogK
      for (pair<const T, queue<int>> &kv : shelf) {
        auto &block = kv.second;
        while (not block.empty())
          initial.emplace_back(kv.first, block.front()), block.pop();
      }
      int uid = 0, val = initial[0].first;
      pow2ranks.emplace_back(), pow2ranks.back().resize(n);
      trav(e, initial) { // N
        if (val < e.first)
          uid++;
        pow2ranks[0][e.second] = uid, val = e.first;
      }
    }
    int pow = 0, sz = 1;
    vector<queue<pair<pi, int>>> shelf(n); //(rank1,rank2),index
    while (sz < n) {                       // logN loops
      int newpow = pow + 1, newsz = sz * 2;
      pow2ranks.emplace_back(), pow2ranks.back().resize(n);
      auto &oldrank = pow2ranks[pow], &newrank = pow2ranks[newpow];
      vector<pair<pi, int>> tobesorted;
      f0r(i, n) { // N
        int j = sanitize(i + sz);
        tobesorted.emplace_back(mp(mp(oldrank[i], oldrank[j]), i));
      }
      trav(e, tobesorted) shelf[e.first.second].emplace(e); // N
      tobesorted.clear();
      trav(block, shelf) while (not block.empty()) {
        auto e = block.front();
        block.pop();
        tobesorted.emplace_back(e);
      }
      trav(e, tobesorted) shelf[e.first.first].emplace(e); // N
      tobesorted.clear();
      trav(block, shelf) while (not block.empty()) {
        auto e = block.front();
        block.pop();
        tobesorted.emplace_back(e);
      }
      int uid = 0;
      pi val = tobesorted[0].first;
      trav(e, tobesorted) {
        if (val < e.first)
          uid++;
        newrank[e.second] = uid, val = e.first;
      }
      pow = newpow, sz = newsz;
    }
  }

  inline int sanitize(int i) {
    int excess = max(i - n + 1, 0);
    i -= ((excess % loop > 0) + (excess / loop)) * loop;
    return i;
  }

  inline pair<int, int> query(int i, int len = -1) { // log len time
    i = sanitize(i);
    if (len == -1) {
      return mp(pow2ranks.back()[i], pow2ranks.back()[i]);
    }
    if (len == 0) {
      return mp(0, 0);
    } else {
      int sz = 1, pow = 0;
      while ((sz << 1) < len)
        sz = sz << 1, pow++; // log len time
      int j = sanitize(i + len - sz);
      return mp(pow2ranks[pow][i], pow2ranks[pow][j]);
    }
  }
};

auto __tic__ = chrono::high_resolution_clock::now();

void tic() { __tic__ = chrono::high_resolution_clock::now(); }

int toc() {
  int elapsed = chrono::duration_cast<chrono::microseconds>(
                    chrono::high_resolution_clock::now() - __tic__)
                    .count();
  return elapsed;
}

void precalc() {
  // start here
}

// helper fuctions here

void solve(int ti) {
  // start here
  int n, m;
  re(n, m);
  vpi facts(m);
  re(facts);
  trav(f, facts) f.first--, f.second--;
  vi repr(n);
  f0r(i, n) repr[i] = i;
  vi weight(n, 1);
  trav(fact, facts) {
    int f, s;
    tie(f, s) = fact;
    while (repr[f] != f)
      f = repr[f];
    while (repr[s] != s)
      s = repr[s];
    if (weight[f] > weight[s])
      swap(f, s);
    repr[f] = repr[s], weight[s] += weight[f];
  }
  map<int, int> rep2count;
  f0r(i, n) {
    int type = i;
    while (repr[type] != type)
      type = repr[type];
    rep2count[type]++;
  }
  int best = 0;
  trav(kv, rep2count) ckmax(best, kv.second);
  ps(best);
}

int main() {
  precalc();
  bool online = true;
#ifdef OFFLINE
  online = false;
  if (online)
    boost();
  string testinputs[] = {
      R"(
10 4
3 1
4 1
5 9
2 6
)",
      //            R"(3 2
      // 1 1 0
      // 1 2
      // 1 3
      //
      //)",
  }; // TODO
  trav(testinput, testinputs) {
    istringstream iss(testinput);
    cout << "---local mode---" << endl;
    cin.rdbuf(iss.rdbuf());
#endif
    // setIO("A");
    int T = 1;
    {
      //            re(T);23
    }
    vfor(i, 1, T + 1) {
      //        cout << "Case #" << i << ": ";//Google Code jam
      solve(i);
    }

#ifdef OFFLINE
  }
#endif
}

Fixed submission:
using namespace std;

#include <bits/stdc++.h>

typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;

typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<db, db> pd;

typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;

typedef set<int> si;
typedef set<ll> sl;
typedef map<int, int> mii;

#define mp make_pair
#define sz(x) (int)x.size()
#define len(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
// #define pf push_front
// #define pb push_back
#define eb emplace_back
#define ep emplace
#define lb lower_bound
#define ub upper_bound

#define vfor(i, a, b) for (int i = (a); i < (b); ++i)
#define f0r(i, a) vfor(i, 0, a)
#define rof(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define r0f(i, a) rof(i, 0, a)
#define trav(a, x) for (auto &a : x)
#define def(fname, rtype, args, ...)                                           \
  function<rtype args> fname = [__VA_ARGS__] args

#define boost() cin.tie(0), cin.sync_with_stdio(0)

template <class T>
void binstf(T &found, T a, T b, function<bool(T)> test, bool TF = true) {
  T i = a, j = b;
  bool da = test(a), db = test(b);
  if ((da != TF) or (db == TF)) {
    cerr << "---[BS: TF = " << TF << "]---" << endl;
    cerr << a << "->" << da << endl;
    cerr << b << "->" << db << endl;
  }
  while (j - i > 1) {
    T m = (i + j) / 2;
    if (test(m) == TF)
      i = m;
    else
      j = m;
  }
  found = i;
  if (not TF)
    found++;
}

#define binsft(a, b, c, d) binstf(a, b, c, d, false);

template <class T> T dpow(T a, T power) {
  T result = 1;
  while (power) {
    if (power % 2)
      result *= a;
    power /= 2, a = a * a;
  }
  return result;
}

const ld PI = acos((ld)-1);
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());

template <class T> bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }

template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

template <class T> bool reorder(T &a, T &b) {
  return (a > b) ? swap(a, b), 1 : 0;
}

// INPUT
template <class A> void re(complex<A> &c);

template <class A, class B> void re(pair<A, B> &p);

template <class A> void re(vector<A> &v);

template <class A, size_t SZ> void re(array<A, SZ> &a);

#define ore(type, x)                                                           \
  type x;                                                                      \
  re(x);
#define ire(x) ore(int, x);
#define vire(x) ore(vi, x);
#define lre(x) ore(ll, x);

template <class T> void re(T &x) { cin >> x; }

void re(db &d) {
  str t;
  re(t);
  d = stod(t);
}

void re(ld &d) {
  str t;
  re(t);
  d = stold(t);
}

template <class H, class... T> void re(H &h, T &...t) {
  re(h);
  re(t...);
}

template <class A> void re(complex<A> &c) {
  A a, b;
  re(a, b);
  c = {a, b};
}

template <class A, class B> void re(pair<A, B> &p) { re(p.first, p.second); }

template <class A> void re(vector<A> &x) { trav(a, x) re(a); }

template <class A, size_t SZ> void re(array<A, SZ> &x) { trav(a, x) re(a); }

template <class T> T gcd(T a, T b) {
  a = a < 0 ? -a : a;
  b = b < 0 ? -b : b;
  if (a * b == 0)
    return max(a, b);
  else
    return gcd(min(a, b), max(a, b) % min(a, b));
}

const int MODE107 = 1000000007;

template <class T> T modop(T a, T mode = MODE107) {
  a = a % mode;
  if (a < 0)
    a += mode;
  return a;
}

template <class T> T inv(T a, T mode = MODE107) {
  T coefa = 1, coefb = 0;
  T aa = a, bb = mode;
  while (aa != 1) {
    if (aa > bb)
      swap(coefa, coefb), swap(aa, bb);
    T cc = bb / aa;
    bb -= cc * aa, coefb -= cc * coefa;
    swap(coefa, coefb), swap(aa, bb);
  }
  return coefa;
}

const int uplrDX[] = {-1, 1, 0, 0};
const int uplrDY[] = {0, 0, -1, 1};

#define ts to_string

str ts(char c) { return str(1, c); }

str ts(bool b) { return b ? "true" : "false"; }

str ts(const char *s) { return (str)s; }

str ts(str s) { return s; }

template <class A> str ts(complex<A> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}

str ts(vector<bool> v) {
  str res = "{";
  f0r(i, sz(v)) res += char('0' + v[i]);
  res += "}";
  return res;
}

template <size_t SZ> str ts(bitset<SZ> b) {
  str res = "";
  f0r(i, SZ) res += char('0' + b[i]);
  return res;
}

template <class A, class B> str ts(pair<A, B> p);

template <class T> str ts(T v) { // containers with begin(), end()
  bool fst = 1;
  str res = "{";
  for (const auto &x : v) {
    if (!fst)
      res += ", ";
    fst = 0;
    res += ts(x);
  }
  res += "}";
  return res;
}

template <class A, class B> str ts(pair<A, B> p) {
  return "(" + ts(p.first) + ", " + ts(p.second) + ")";
}

// OUTPUT
template <class A> void pr(A x) { cout << ts(x); }

template <class H, class... T> void pr(const H &h, const T &...t) {
  pr(h);
  pr(t...);
}

void ps() { pr("\n"); } // print w/ spaces
template <class H, class... T> void ps(const H &h, const T &...t) {
  pr(h);
  if (sizeof...(t))
    pr(" ");
  ps(t...);
}

// DEBUG
void DBG() { cerr << "]" << endl; }

template <class H, class... T> void DBG(H h, T... t) {
  cerr << ts(h);
  if (sizeof...(t))
    cerr << ", ";
  DBG(t...);
}

#ifdef LOCAL // compile with -DLOCAL
#define dbg(...)                                                               \
  cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",           \
      DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif

// REINITIALIZE ARRAYS BETWEEN TCs

/**
 * Description: Use in place of \texttt{complex<T>}.
 * Source: http://codeforces.com/blog/entry/22175, KACTL
 * Verification: various
 */

typedef int T;

int sgn(T a) { return (a > 0) - (a < 0); }

T sq(T a) { return a * a; }

// using namespace Point;

typedef unsigned long long ull;

class trie {
public:
  map<char, trie> l;

  void add(string t) {
    if (t.length() > 0) {
      l[t[0]].add(t.substr(1));
    }
  }

  bool contains(string t) {
    if (not l.count(t[0]))
      return false;
    return l[t[0]].contains(t.substr(1));
  }
};

template <class T> class rq {
  /* range query
   */
  vector<vector<T>> content;
  function<T(T, T)> op;

public:
  rq(vector<T> &orig, function<T(T, T)> operation) {
    op = operation;
    int size = 1;
    content.emplace_back(orig);
    while (size < orig.size()) {
      size *= 2;
      content.emplace_back(0);
      auto &todo = content.back(), &from = content[content.size() - 2];
      f0r(i, sz(from) - size / 2) {
        todo.eb(op(from[i],
                   from[i + size / 2])); //[i ~ i+s[ = [i, i+s/2[ + [i+s/2,i+s[
      }
    }
  }

  T query(int i, int j) { //[i,j[
    if (j <= i or j > content[0].size() or i < 0 or i >= content[0].size()) {
      cerr << "i=" << i << endl;
      cerr << "j=" << j << endl;
      throw "bad i j";
    }
    tie(i, j) = mp(min(i, j), max(i, j));
    int size = 1, pow = 0;
    while (size * 2 < j - i) {
      size *= 2, pow++;
    }
    assert(pow < content.size());
    auto &c = content[pow];
    assert(i < c.size() and i >= 0);
    assert(j - size < c.size() and j - size >= 0);
    T dbg = op(content[pow][i], content[pow][j - size]);
    return dbg;
  }
};

template <class T> class maxflow {
public:
  typedef T unit;
  int src, drn; // source and drain node id
  vector<vi> adj, radj;
  map<pi, unit> lims;
  map<pi, unit> rlims; // will contain solution after solve()
  void genradj() {
    radj.resize(sz(adj));
    f0r(from, sz(adj)) {
      trav(to, adj[from]) { radj[to].emplace_back(from); }
    }
  }

  unit solve() {
    while (true) {
      map<int, pair<pi, unit>> backtrack;
      bool found = false;
      set<int> seen; // bfs from src
      queue<pair<int, unit>> todo;
      todo.emplace(src, -1);
      while (not todo.empty()) {
        int from = todo.front().first;
        unit bottleneck = todo.front().second;
        todo.pop();
        if (from == drn) {
          found = true;
          break;
        }
        trav(to, adj[from]) {
          pi edge = mp(from, to);
          unit bn = min(bottleneck, lims[edge]);
          if (bn and not seen.count(to)) {
            seen.emplace(to);
            todo.emplace(to, bn);
            backtrack[to] = mp(edge, bn);
          }
        }

        trav(to, radj[from]) {
          pi edge = mp(to, from);
          unit bn = min(bottleneck, rlims[edge]);
          if (bn and not seen.count(to)) {
            seen.emplace(to);
            todo.emplace(to, bn);
            backtrack[to] = mp(edge, bn);
          }
        }
      }
      if (not found)
        break;
      else {
        list<pi> edges;
        int to = drn;
        unit flow = backtrack[to].second;
        while (to != src) {
          pi edge = backtrack[to].first;
          int from = edge.first + edge.second - to;
          edges.emplace_front(edge);
          to = from;
        }
        int from = src;
        trav(e, edges) {
          if (e.first == from)
            rlims[e] += flow, lims[e] -= flow;
          else
            rlims[e] -= flow, lims[e] += flow;
          from = e.first + e.second - from;
        }
      }
    }
    unit res = 0;
    trav(to, adj[src]) res += rlims[mp(src, to)];
    return res;
  }
};

template <class T> class SuffArr {
public:
  vector<vi> pow2ranks;
  int loop;
  int n;

  SuffArr() {}

  SuffArr(vector<T> &in, int loop_) { reset(in, loop_); }

  SuffArr(string &in, int loop_) {
    vector<T> cached;
    trav(c, in) cached.emplace_back(c);
    reset(cached, loop_);
  }

  void reset(string &in, int loop_) {
    vector<T> cached;
    trav(c, in) cached.emplace_back(c);
    reset(cached, loop_);
  }

  void reset(vector<T> &in, int loop_) { // N chars in charspace K
    loop = loop_, n = in.size();
    pow2ranks.clear();
    {
      vector<pair<T, int>> initial;
      map<T, queue<int>> shelf;
      f0r(i, n) shelf[in[i]].emplace(i); // logK per write, NlogK
      for (pair<const T, queue<int>> &kv : shelf) {
        auto &block = kv.second;
        while (not block.empty())
          initial.emplace_back(kv.first, block.front()), block.pop();
      }
      int uid = 0, val = initial[0].first;
      pow2ranks.emplace_back(), pow2ranks.back().resize(n);
      trav(e, initial) { // N
        if (val < e.first)
          uid++;
        pow2ranks[0][e.second] = uid, val = e.first;
      }
    }
    int pow = 0, sz = 1;
    vector<queue<pair<pi, int>>> shelf(n); //(rank1,rank2),index
    while (sz < n) {                       // logN loops
      int newpow = pow + 1, newsz = sz * 2;
      pow2ranks.emplace_back(), pow2ranks.back().resize(n);
      auto &oldrank = pow2ranks[pow], &newrank = pow2ranks[newpow];
      vector<pair<pi, int>> tobesorted;
      f0r(i, n) { // N
        int j = sanitize(i + sz);
        tobesorted.emplace_back(mp(mp(oldrank[i], oldrank[j]), i));
      }
      trav(e, tobesorted) shelf[e.first.second].emplace(e); // N
      tobesorted.clear();
      trav(block, shelf) while (not block.empty()) {
        auto e = block.front();
        block.pop();
        tobesorted.emplace_back(e);
      }
      trav(e, tobesorted) shelf[e.first.first].emplace(e); // N
      tobesorted.clear();
      trav(block, shelf) while (not block.empty()) {
        auto e = block.front();
        block.pop();
        tobesorted.emplace_back(e);
      }
      int uid = 0;
      pi val = tobesorted[0].first;
      trav(e, tobesorted) {
        if (val < e.first)
          uid++;
        newrank[e.second] = uid, val = e.first;
      }
      pow = newpow, sz = newsz;
    }
  }

  inline int sanitize(int i) {
    int excess = max(i - n + 1, 0);
    i -= ((excess % loop > 0) + (excess / loop)) * loop;
    return i;
  }

  inline pair<int, int> query(int i, int len = -1) { // log len time
    i = sanitize(i);
    if (len == -1) {
      return mp(pow2ranks.back()[i], pow2ranks.back()[i]);
    }
    if (len == 0) {
      return mp(0, 0);
    } else {
      int sz = 1, pow = 0;
      while ((sz << 1) < len)
        sz = sz << 1, pow++; // log len time
      int j = sanitize(i + len - sz);
      return mp(pow2ranks[pow][i], pow2ranks[pow][j]);
    }
  }
};

auto __tic__ = chrono::high_resolution_clock::now();

void tic() { __tic__ = chrono::high_resolution_clock::now(); }

int toc() {
  int elapsed = chrono::duration_cast<chrono::microseconds>(
                    chrono::high_resolution_clock::now() - __tic__)
                    .count();
  return elapsed;
}

void precalc() {
  // start here
}

// helper fuctions here

void solve(int ti) {
  // start here
  int n, m;
  re(n, m);
  vpi facts(m);
  re(facts);
  trav(f, facts) f.first--, f.second--;
  vi repr(n);
  f0r(i, n) repr[i] = i;
  vi weight(n, 1);
  trav(fact, facts) {
    int f, s;
    tie(f, s) = fact;
    while (repr[f] != f)
      f = repr[f];
    while (repr[s] != s)
      s = repr[s];
    if (f == s)
      continue;
    if (weight[f] > weight[s])
      swap(f, s);
    repr[f] = repr[s], weight[s] += weight[f];
  }
  map<int, int> rep2count;
  f0r(i, n) {
    int type = i;
    while (repr[type] != type)
      type = repr[type];
    rep2count[type]++;
  }
  int best = 0;
  trav(kv, rep2count) ckmax(best, kv.second);
  ps(best);
}

int main() {
  precalc();
  bool online = true;
#ifdef OFFLINE
  online = false;
  if (online)
    boost();
  string testinputs[] = {
      R"(
10 4
3 1
4 1
5 9
2 6
)",
      //            R"(3 2
      // 1 1 0
      // 1 2
      // 1 3
      //
      //)",
  }; // TODO
  trav(testinput, testinputs) {
    istringstream iss(testinput);
    cout << "---local mode---" << endl;
    cin.rdbuf(iss.rdbuf());
#endif
    // setIO("A");
    int T = 1;
    {
      //            re(T);23
    }
    vfor(i, 1, T + 1) {
      //        cout << "Case #" << i << ": ";//Google Code jam
      solve(i);
    }

#ifdef OFFLINE
  }
#endif
}