Problem p02539 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
// using namespace atcoder;
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  {                                                                            \
    cout << #v << "=" << endl;                                                 \
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \
    cout << endl;                                                              \
  }
#define mdebug(m)                                                              \
  {                                                                            \
    cout << #m << "=" << endl;                                                 \
    REP(i_debug, m.size()) {                                                   \
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \
      cout << endl;                                                            \
    }                                                                          \
  }
#define pb push_back
#define fi first
#define se second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void chOut(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using v_bool = vector<bool>;
using v_Pii = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

// const int mod = 1000000007;
const int mod = 998244353;

template <long long MOD> struct ModInt {

  using ll = long long;
  ll val;

  void setval(ll v) { val = v % MOD; };
  ModInt() : val(0) {}
  ModInt(ll v) { setval(v); };

  ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
  ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
  ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
  ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
  ModInt operator-() const { return ModInt(MOD - val); }
  ModInt operator+=(const ModInt &x) { return *this = *this + x; }
  ModInt operator-=(const ModInt &x) { return *this = *this - x; }
  ModInt operator*=(const ModInt &x) { return *this = *this * x; }
  ModInt operator/=(const ModInt &x) { return *this = *this / x; }
  bool operator==(const ModInt &x) const { return (*this).val == x.val; }

  friend ostream &operator<<(ostream &os, const ModInt &x) {
    os << x.val;
    return os;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    is >> x.val;
    x.val = (x.val % MOD + MOD) % MOD;
    return is;
  }

  ModInt pow(ll n) const {
    ModInt a = 1;
    if (n == 0)
      return a;
    int i0 = 64 - __builtin_clzll(n);
    for (int i = i0 - 1; i >= 0; i--) {
      a = a * a;
      if ((n >> i) & 1)
        a *= (*this);
    }
    return a;
  }
  ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>;
mint pow(mint x, long long n) { return x.pow(n); }
// using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination {

  vector<mint> fact, invfact;

  Combination(int N) {
    fact = vector<mint>({mint(1)});
    invfact = vector<mint>({mint(1)});
    fact_initialize(N);
  }

  void fact_initialize(int N) {
    int i0 = fact.size();
    if (i0 >= N + 1)
      return;
    fact.resize(N + 1);
    invfact.resize(N + 1);
    for (int i = i0; i <= N; i++)
      fact[i] = fact[i - 1] * i;
    invfact[N] = (mint)1 / fact[N];
    for (int i = N - 1; i >= i0; i--)
      invfact[i] = invfact[i + 1] * (i + 1);
  }

  mint nCr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[r] * invfact[n - r];
  }

  mint nPr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[n - r];
  }

  mint Catalan(int n) {
    if (n < 0)
      return 0;
    else if (n == 0)
      return 1;
    if (fact.size() < 2 * n + 1)
      fact_initialize(2 * n);
    return fact[2 * n] * invfact[n + 1] * invfact[n];
  }
};

template <long long MOD> class NTT {
private:
  vector<ModInt<MOD>> f, f_tmp;

  void init() {
    n = 31 - __builtin_clz((signed)N);
    assert(N == (1 << n));

    assert((e.pow(N)).val == 1);
    pow_e.resize(N + 1);
    pow_e[0] = 1;
    bool e_valid = true;
    FOR(i, 1, N) {
      pow_e[i] = pow_e[i - 1] * e;
      if (pow_e[i].val == 1)
        e_valid = false;
    }
    pow_e[N] = 1;
    assert(e_valid);

    inv_N = ((ModInt<MOD>)N).inv();

    f.resize(N);
    f_tmp.resize(N);
  }

  void forward_exec(int l, int r, int t) {
    if (t == n)
      return;
    int sz = (r - l) >> 1;
    REP(i, sz) {
      f_tmp[l + i] = f[l + 2 * i];
      f_tmp[l + sz + i] = f[l + 2 * i + 1];
    }
    FOR(i, l, r) f[i] = f_tmp[i];
    forward_exec(l, l + sz, t + 1);
    forward_exec(l + sz, r, t + 1);

    REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[i << t];
    REP(i, sz)
    f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[(sz + i) << t];
    FOR(i, l, r) f[i] = f_tmp[i];
  }

  void inverse_exec(int l, int r, int t) {
    if (t == n)
      return;
    int sz = (r - l) / 2;
    REP(i, sz) {
      f_tmp[l + i] = f[l + 2 * i];
      f_tmp[l + sz + i] = f[l + 2 * i + 1];
    }
    FOR(i, l, r) f[i] = f_tmp[i];
    inverse_exec(l, l + sz, t + 1);
    inverse_exec(l + sz, r, t + 1);

    REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[N - (i << t)];
    REP(i, sz)
    f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[N - ((sz + i) << t)];
    FOR(i, l, r) f[i] = f_tmp[i];
  }

public:
  int N, n;
  ModInt<MOD> e, inv_N;
  vector<ModInt<MOD>> pow_e;

  // array size M is converted to N = 2^n (>=M)
  // only for MOD = 924844033, 998244353, 1012924417
  NTT(int M) {
    N = 1;
    while (M > N)
      N <<= 1;

    ModInt<MOD> x;
    if (MOD == 924844033)
      x = 5;
    else if (MOD == 998244353)
      x = 3;
    else if (MOD == 1012924417)
      x = 5;
    else
      assert(false);

    assert((MOD - 1) % N == 0);
    e = x.pow((MOD - 1) / N);

    init();
  }

  // N=2^n, e^N=1, e^k!=1 (k<N) must be satisfied
  NTT(int N, ModInt<MOD> e) : N(N), e(e) { init(); }

  void exec(vector<ModInt<MOD>> &F, bool inverse = false) {
    assert(F.size() == N);
    f.swap(F);
    if (!inverse)
      forward_exec(0, N, 0);
    else
      inverse_exec(0, N, 0);
    F.swap(f);
    if (inverse) {
      REP(i, N) F[i] *= inv_N;
    }
  }

  // if resize_result is true, the array size of the result becomes A.size() +
  // B.size() - 1 array size must be equal to N if negetive indices are included
  vector<ModInt<MOD>> convolution(vector<ModInt<MOD>> A, vector<ModInt<MOD>> B,
                                  bool resize_result = false) {
    int sA = A.size(), sB = B.size();
    assert(sA <= N && sB <= N);
    A.resize(N);
    B.resize(N);
    exec(A);
    exec(B);

    vector<ModInt<MOD>> C(N);
    REP(i, N) C[i] = A[i] * B[i];
    exec(C, true);

    if (resize_result)
      C.resize(sA + sB - 1);

    return C;
  }
};

signed main() {

  int N;
  cin >> N;
  vec h(2 * N);
  cin >> h;
  const int M = 100000;
  vec cnt(M);
  REP(i, 2 * N) cnt[h[i] - 1]++;

  Combination C(M);
  mvec G(M + 1);
  G[0] = 1;
  FOR(i, 2, M + 1) if (i % 2 == 0) G[i] = G[i - 2] * (i - 1);

  mmat S;
  priority_queue<Pii, vector<Pii>, greater<Pii>> que;
  int id = 0;
  REP(i, M) if (cnt[i] >= 2) {
    mvec tmp(cnt[i] / 2 + 1);
    REP(n, cnt[i] / 2 + 1) tmp[n] = C.nCr(cnt[i], 2 * n) * G[2 * n];
    S.pb(tmp);
    que.push(Pii(SZ(tmp), id));
    id++;
  }

  while (que.size() >= 2) {
    Pii p1 = que.top();
    que.pop();
    Pii p2 = que.top();
    que.pop();
    NTT<mod> ntt(p1.fi + p2.fi - 1);
    mvec tmp = ntt.convolution(S[p1.se], S[p2.se], true);
    S.pb(tmp);
    que.push(Pii(SZ(tmp), id));
    id++;
  }

  mint ans = 0;
  mvec num = S.back();
  REP(i, SZ(num)) {
    if (i % 2 == 0)
      ans += G[2 * (N - i)] * num[i];
    else
      ans -= G[2 * (N - i)] * num[i];
  }
  Out(ans);

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
// using namespace atcoder;
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  {                                                                            \
    cout << #v << "=" << endl;                                                 \
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \
    cout << endl;                                                              \
  }
#define mdebug(m)                                                              \
  {                                                                            \
    cout << #m << "=" << endl;                                                 \
    REP(i_debug, m.size()) {                                                   \
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \
      cout << endl;                                                            \
    }                                                                          \
  }
#define pb push_back
#define fi first
#define se second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void chOut(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using v_bool = vector<bool>;
using v_Pii = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

// const int mod = 1000000007;
const int mod = 998244353;

template <long long MOD> struct ModInt {

  using ll = long long;
  ll val;

  void setval(ll v) { val = v % MOD; };
  ModInt() : val(0) {}
  ModInt(ll v) { setval(v); };

  ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
  ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
  ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
  ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
  ModInt operator-() const { return ModInt(MOD - val); }
  ModInt operator+=(const ModInt &x) { return *this = *this + x; }
  ModInt operator-=(const ModInt &x) { return *this = *this - x; }
  ModInt operator*=(const ModInt &x) { return *this = *this * x; }
  ModInt operator/=(const ModInt &x) { return *this = *this / x; }
  bool operator==(const ModInt &x) const { return (*this).val == x.val; }

  friend ostream &operator<<(ostream &os, const ModInt &x) {
    os << x.val;
    return os;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    is >> x.val;
    x.val = (x.val % MOD + MOD) % MOD;
    return is;
  }

  ModInt pow(ll n) const {
    ModInt a = 1;
    if (n == 0)
      return a;
    int i0 = 64 - __builtin_clzll(n);
    for (int i = i0 - 1; i >= 0; i--) {
      a = a * a;
      if ((n >> i) & 1)
        a *= (*this);
    }
    return a;
  }
  ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>;
mint pow(mint x, long long n) { return x.pow(n); }
// using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination {

  vector<mint> fact, invfact;

  Combination(int N) {
    fact = vector<mint>({mint(1)});
    invfact = vector<mint>({mint(1)});
    fact_initialize(N);
  }

  void fact_initialize(int N) {
    int i0 = fact.size();
    if (i0 >= N + 1)
      return;
    fact.resize(N + 1);
    invfact.resize(N + 1);
    for (int i = i0; i <= N; i++)
      fact[i] = fact[i - 1] * i;
    invfact[N] = (mint)1 / fact[N];
    for (int i = N - 1; i >= i0; i--)
      invfact[i] = invfact[i + 1] * (i + 1);
  }

  mint nCr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[r] * invfact[n - r];
  }

  mint nPr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[n - r];
  }

  mint Catalan(int n) {
    if (n < 0)
      return 0;
    else if (n == 0)
      return 1;
    if (fact.size() < 2 * n + 1)
      fact_initialize(2 * n);
    return fact[2 * n] * invfact[n + 1] * invfact[n];
  }
};

template <long long MOD> class NTT {
private:
  vector<ModInt<MOD>> f, f_tmp;

  void init() {
    n = 31 - __builtin_clz((signed)N);
    assert(N == (1 << n));

    assert((e.pow(N)).val == 1);
    pow_e.resize(N + 1);
    pow_e[0] = 1;
    bool e_valid = true;
    FOR(i, 1, N) {
      pow_e[i] = pow_e[i - 1] * e;
      if (pow_e[i].val == 1)
        e_valid = false;
    }
    pow_e[N] = 1;
    assert(e_valid);

    inv_N = ((ModInt<MOD>)N).inv();

    f.resize(N);
    f_tmp.resize(N);
  }

  void forward_exec(int l, int r, int t) {
    if (t == n)
      return;
    int sz = (r - l) >> 1;
    REP(i, sz) {
      f_tmp[l + i] = f[l + 2 * i];
      f_tmp[l + sz + i] = f[l + 2 * i + 1];
    }
    FOR(i, l, r) f[i] = f_tmp[i];
    forward_exec(l, l + sz, t + 1);
    forward_exec(l + sz, r, t + 1);

    REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[i << t];
    REP(i, sz)
    f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[(sz + i) << t];
    FOR(i, l, r) f[i] = f_tmp[i];
  }

  void inverse_exec(int l, int r, int t) {
    if (t == n)
      return;
    int sz = (r - l) / 2;
    REP(i, sz) {
      f_tmp[l + i] = f[l + 2 * i];
      f_tmp[l + sz + i] = f[l + 2 * i + 1];
    }
    FOR(i, l, r) f[i] = f_tmp[i];
    inverse_exec(l, l + sz, t + 1);
    inverse_exec(l + sz, r, t + 1);

    REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[N - (i << t)];
    REP(i, sz)
    f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[N - ((sz + i) << t)];
    FOR(i, l, r) f[i] = f_tmp[i];
  }

public:
  int N, n;
  ModInt<MOD> e, inv_N;
  vector<ModInt<MOD>> pow_e;

  // array size M is converted to N = 2^n (>=M)
  // only for MOD = 924844033, 998244353, 1012924417
  NTT(int M) {
    N = 1;
    while (M > N)
      N <<= 1;

    ModInt<MOD> x;
    if (MOD == 924844033)
      x = 5;
    else if (MOD == 998244353)
      x = 3;
    else if (MOD == 1012924417)
      x = 5;
    else
      assert(false);

    assert((MOD - 1) % N == 0);
    e = x.pow((MOD - 1) / N);

    init();
  }

  // N=2^n, e^N=1, e^k!=1 (k<N) must be satisfied
  NTT(int N, ModInt<MOD> e) : N(N), e(e) { init(); }

  void exec(vector<ModInt<MOD>> &F, bool inverse = false) {
    assert(F.size() == N);
    f.swap(F);
    if (!inverse)
      forward_exec(0, N, 0);
    else
      inverse_exec(0, N, 0);
    F.swap(f);
    if (inverse) {
      REP(i, N) F[i] *= inv_N;
    }
  }

  // if resize_result is true, the array size of the result becomes A.size() +
  // B.size() - 1 array size must be equal to N if negetive indices are included
  vector<ModInt<MOD>> convolution(vector<ModInt<MOD>> A, vector<ModInt<MOD>> B,
                                  bool resize_result = false) {
    int sA = A.size(), sB = B.size();
    assert(sA <= N && sB <= N);
    A.resize(N);
    B.resize(N);
    exec(A);
    exec(B);

    vector<ModInt<MOD>> C(N);
    REP(i, N) C[i] = A[i] * B[i];
    exec(C, true);

    if (resize_result)
      C.resize(sA + sB - 1);

    return C;
  }
};

signed main() {

  int N;
  cin >> N;
  vec h(2 * N);
  cin >> h;
  const int M = 100000;
  vec cnt(M);
  REP(i, 2 * N) cnt[h[i] - 1]++;

  Combination C(M);
  mvec G(M + 1);
  G[0] = 1;
  FOR(i, 2, M + 1) if (i % 2 == 0) G[i] = G[i - 2] * (i - 1);

  mmat S;
  priority_queue<Pii, vector<Pii>, greater<Pii>> que;
  int id = 0;
  REP(i, M) if (cnt[i] >= 2) {
    mvec tmp(cnt[i] / 2 + 1);
    REP(n, cnt[i] / 2 + 1) tmp[n] = C.nCr(cnt[i], 2 * n) * G[2 * n];
    S.pb(tmp);
    que.push(Pii(SZ(tmp), id));
    id++;
  }

  while (que.size() >= 2) {
    Pii p1 = que.top();
    que.pop();
    Pii p2 = que.top();
    que.pop();
    NTT<mod> ntt(p1.fi + p2.fi - 1);
    mvec tmp = ntt.convolution(S[p1.se], S[p2.se], true);
    S.pb(tmp);
    que.push(Pii(SZ(tmp), id));
    id++;
  }

  mint ans = 0;
  if (SZ(S)) {
    mvec num = S.back();
    REP(i, SZ(num)) {
      if (i % 2 == 0)
        ans += G[2 * (N - i)] * num[i];
      else
        ans -= G[2 * (N - i)] * num[i];
    }
  } else {
    ans = G[2 * N];
  }
  Out(ans);

  return 0;
}