Problem p02866 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;

typedef unsigned long ul;
typedef unsigned long long ull;
typedef long long ll;
typedef vector<ll> vint;
typedef vector<vector<ll>> vvint;
typedef vector<vector<vector<ll>>> vvvint;
typedef vector<string> vstring;
typedef vector<vector<string>> vvstring;
typedef vector<char> vchar;
typedef vector<vector<char>> vvchar;
typedef vector<long double> vdouble;
typedef vector<vector<long double>> vvdouble;
typedef vector<vector<vector<long double>>> vvvdouble;
typedef pair<ll, ll> pint;
typedef vector<pint> vpint;
typedef vector<bool> vbool;

#define rep(i, n) for (ll i = 0; i < n; i++)
#define repf(i, f, n) for (ll i = f; i < n; i++)
#define repr(i, n) for (ll i = n - 1; i >= 0; i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define ALL(obj) (obj).begin(), (obj).end()
// #define LLONG_MAX 9223372036854775806
#define vmax(vec) *max_element(vec.begin(), vec.end())
#define vmin(vec) *min_element(vec.begin(), vec.end())
#define vsort(vec) sort(vec.begin(), vec.end())
#define vsortgr(vec) sort(vec.begin(), vec.end(), greater<ll>())
// #define MOD 1000000007
#define MOD 998244353

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

//
// struct Node{
//   vint children;
//   ll index;
//   ll prop;
// };
// struct edge{ll to; ll cost;};

int dy[] = {0, 0, 1, -1};
int dx[] = {
    1,
    -1,
    0,
    0,
};

template <typename T> struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T> using Matrix = vector<vector<T>>;

ll gcd(ll a, ll b) {
  if (a < b) {
    a ^= b;
    b ^= a;
    a ^= b;
  }

  return b ? gcd(b, a % b) : a;
}

ll lcm(int a, ll b) { return a * b / gcd(a, b); }

// 繰り返し二乗法
ll power(ll a, ll b) {
  if (a == 1)
    return a;
  // if(a==0)re
  ll res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % MOD;
    a = a * a % MOD;
    b >>= 1;
  }
  return res;
}

const int MAX = 510000;

ll fact[MAX], fact_inv[MAX];

void init_fact(ll n) {
  fact[0] = 1;
  // 階乗の計算
  rep(i, n) fact[i + 1] = fact[i] * (i + 1) % MOD;
  fact_inv[n] = power(fact[n], MOD - 2);
  // 逆元の計算
  for (ll i = n - 1; i >= 0; i--)
    fact_inv[i] = fact_inv[i + 1] * (i + 1) % MOD;
}

ll comb(ll n, ll r) {
  return (fact[n] * fact_inv[r]) % MOD * fact_inv[n - r] % MOD;
}

ll perm(ll n, ll r) { return (fact[n] * fact_inv[n - r]) % MOD; }

struct UnionFind {
  vector<ll> par; // par[i]:iの親の番号　(例) par[3] = 2 : 3の親が2
  vector<ll> num;
  // vector<ll> dist; // rootまでの距離

  UnionFind(ll N) : par(N), num(N) { // 最初は全てが根であるとして初期化
    for (ll i = 0; i < N; i++)
      par[i] = i;
    for (ll i = 0; i < N; i++)
      num[i] = 1;
    // for(ll i = 0; i < N; i++) dist[i] = 0;
  }

  ll root(ll x) { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
    if (par[x] == x)
      return x;
    return par[x] = root(par[x]);
  }

  void unite(ll x, ll y) { // xとyの木を併合
    ll rx = root(x);       // xの根をrx
    ll ry = root(y);       // yの根をry
    if (rx == ry)
      return; // xとyの根が同じ(=同じ木にある)時はそのまま
    par[rx] =
        ry; // xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
    num[ry] = num[rx] + num[ry];
  }

  bool same(ll x, ll y) { // 2つのデータx, yが属する木が同じならtrueを返す
    ll rx = root(x);
    ll ry = root(y);
    return rx == ry;
  }

  ll size(ll x) { return num[root(x)]; }
};

vint divisor(ll n) { // nの約数
  vint ret;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.pb(i);
      if (i * i != n)
        ret.pb(n / i);
    }
  }
  vsort(ret);
  return ret;
}

ll my_pow(ll x, ll y) {
  ll rtn = 1;
  rep(i, y) rtn *= x;
  return rtn;
}

ll get_digit_in(ll n, ll i) { // i桁目の数字を得る。
  for (ll j = 0; j < i - 1; j++) {
    n /= 10;
  }
  return n % 10;
}

ll get_digit(ll n) {
  ll rtn = 0;
  while (n > 0) {
    n /= 10;
    rtn++;
  }
  return rtn;
}

map<ll, ll> prime_factor(ll n) {
  map<ll, ll> rtn;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      rtn[i]++;
      n /= i;
    }
  }
  if (n != 1)
    rtn[n] = 1;
  return rtn;
}

// nPnの順列に対して処理を実行する
void foreach_permutation(ll n, function<void(ll *)> f) {
  ll indexes[n];
  for (ll i = 0; i < n; i++)
    indexes[i] = i;
  do {
    f(indexes);
  } while (std::next_permutation(indexes, indexes + n));
}

void recursive_comb(ll *indexes, ll s, ll rest, function<void(ll *)> f) {
  if (rest == 0) {
    f(indexes);
  } else {
    if (s < 0)
      return;
    recursive_comb(indexes, s - 1, rest, f);
    indexes[rest - 1] = s;
    recursive_comb(indexes, s - 1, rest - 1, f);
  }
}

// nCkの組み合わせに対して処理を実行する
void foreach_comb(ll n, ll k, function<void(ll *)> f) {
  ll indexes[k];
  recursive_comb(indexes, n - 1, k, f);
}

// nPkの順列に対して処理を実行する
void foreach_permutation(ll n, ll k, function<void(ll *)> f) {
  foreach_comb(n, k, [&](ll *c_indexes) {
    foreach_permutation(k, [&](ll *p_indexes) {
      ll indexes[k];
      for (ll i = 0; i < k; i++) {
        indexes[i] = c_indexes[p_indexes[i]];
      }
      f(indexes);
    });
  });
}

// ll arr[1000500];
// vint primes;

// //エラトステネスの篩
// void Eratosthenes(){
//   ll N = 1000500;
// 	for(ll i = 0; i < N; i++){
// 		arr[i] = 1;
// 	}
// 	for(ll i = 2; i < sqrt(N); i++){
// 		if(arr[i]){
// 			for(ll j = 0; i * (j + 2) < N; j++){
// 				arr[i *(j + 2)] = 0;
// 			}
// 		}
// 	}

// 	for(ll i = 2; i < N; i++){
// 		if(arr[i]){
//       primes.pb(i);
// 			//cout << i << endl;
// 		}
// 	}
// }

void print(vint &V) {
  for (auto e : V)
    cout << e << " ";
  cout << endl;
}

int main() {
  cout << fixed << setprecision(12);

  ll N;
  cin >> N;
  vint D(N);
  rep(i, N) cin >> D[i];

  vint cnt(N, 0);
  rep(i, N) { cnt[D[i]]++; }

  if (D[0] > 0 || cnt[0] > 1) {
    cout << 0 << endl;
    return 0;
  }

  ll ans = 1;
  rep(i, *max_element(ALL(D))) {
    if (cnt[i] == 0) {
      cout << 0 << endl;
      return 0;
    }
    ans *= power(cnt[i], cnt[i + 1]);
    ans %= MOD;
  }

  cout << ans << endl;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;

typedef unsigned long ul;
typedef unsigned long long ull;
typedef long long ll;
typedef vector<ll> vint;
typedef vector<vector<ll>> vvint;
typedef vector<vector<vector<ll>>> vvvint;
typedef vector<string> vstring;
typedef vector<vector<string>> vvstring;
typedef vector<char> vchar;
typedef vector<vector<char>> vvchar;
typedef vector<long double> vdouble;
typedef vector<vector<long double>> vvdouble;
typedef vector<vector<vector<long double>>> vvvdouble;
typedef pair<ll, ll> pint;
typedef vector<pint> vpint;
typedef vector<bool> vbool;

#define rep(i, n) for (ll i = 0; i < n; i++)
#define repf(i, f, n) for (ll i = f; i < n; i++)
#define repr(i, n) for (ll i = n - 1; i >= 0; i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define ALL(obj) (obj).begin(), (obj).end()
// #define LLONG_MAX 9223372036854775806
#define vmax(vec) *max_element(vec.begin(), vec.end())
#define vmin(vec) *min_element(vec.begin(), vec.end())
#define vsort(vec) sort(vec.begin(), vec.end())
#define vsortgr(vec) sort(vec.begin(), vec.end(), greater<ll>())
// #define MOD 1000000007
#define MOD 998244353

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

//
// struct Node{
//   vint children;
//   ll index;
//   ll prop;
// };
// struct edge{ll to; ll cost;};

int dy[] = {0, 0, 1, -1};
int dx[] = {
    1,
    -1,
    0,
    0,
};

template <typename T> struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
template <typename T> using Matrix = vector<vector<T>>;

ll gcd(ll a, ll b) {
  if (a < b) {
    a ^= b;
    b ^= a;
    a ^= b;
  }

  return b ? gcd(b, a % b) : a;
}

ll lcm(int a, ll b) { return a * b / gcd(a, b); }

// 繰り返し二乗法
ll power(ll a, ll b) {
  if (a == 1)
    return a;
  // if(a==0)re
  ll res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % MOD;
    a = a * a % MOD;
    b >>= 1;
  }
  return res;
}

const int MAX = 510000;

ll fact[MAX], fact_inv[MAX];

void init_fact(ll n) {
  fact[0] = 1;
  // 階乗の計算
  rep(i, n) fact[i + 1] = fact[i] * (i + 1) % MOD;
  fact_inv[n] = power(fact[n], MOD - 2);
  // 逆元の計算
  for (ll i = n - 1; i >= 0; i--)
    fact_inv[i] = fact_inv[i + 1] * (i + 1) % MOD;
}

ll comb(ll n, ll r) {
  return (fact[n] * fact_inv[r]) % MOD * fact_inv[n - r] % MOD;
}

ll perm(ll n, ll r) { return (fact[n] * fact_inv[n - r]) % MOD; }

struct UnionFind {
  vector<ll> par; // par[i]:iの親の番号　(例) par[3] = 2 : 3の親が2
  vector<ll> num;
  // vector<ll> dist; // rootまでの距離

  UnionFind(ll N) : par(N), num(N) { // 最初は全てが根であるとして初期化
    for (ll i = 0; i < N; i++)
      par[i] = i;
    for (ll i = 0; i < N; i++)
      num[i] = 1;
    // for(ll i = 0; i < N; i++) dist[i] = 0;
  }

  ll root(ll x) { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
    if (par[x] == x)
      return x;
    return par[x] = root(par[x]);
  }

  void unite(ll x, ll y) { // xとyの木を併合
    ll rx = root(x);       // xの根をrx
    ll ry = root(y);       // yの根をry
    if (rx == ry)
      return; // xとyの根が同じ(=同じ木にある)時はそのまま
    par[rx] =
        ry; // xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
    num[ry] = num[rx] + num[ry];
  }

  bool same(ll x, ll y) { // 2つのデータx, yが属する木が同じならtrueを返す
    ll rx = root(x);
    ll ry = root(y);
    return rx == ry;
  }

  ll size(ll x) { return num[root(x)]; }
};

vint divisor(ll n) { // nの約数
  vint ret;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.pb(i);
      if (i * i != n)
        ret.pb(n / i);
    }
  }
  vsort(ret);
  return ret;
}

ll my_pow(ll x, ll y) {
  ll rtn = 1;
  rep(i, y) rtn *= x;
  return rtn;
}

ll get_digit_in(ll n, ll i) { // i桁目の数字を得る。
  for (ll j = 0; j < i - 1; j++) {
    n /= 10;
  }
  return n % 10;
}

ll get_digit(ll n) {
  ll rtn = 0;
  while (n > 0) {
    n /= 10;
    rtn++;
  }
  return rtn;
}

map<ll, ll> prime_factor(ll n) {
  map<ll, ll> rtn;
  for (ll i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      rtn[i]++;
      n /= i;
    }
  }
  if (n != 1)
    rtn[n] = 1;
  return rtn;
}

// nPnの順列に対して処理を実行する
void foreach_permutation(ll n, function<void(ll *)> f) {
  ll indexes[n];
  for (ll i = 0; i < n; i++)
    indexes[i] = i;
  do {
    f(indexes);
  } while (std::next_permutation(indexes, indexes + n));
}

void recursive_comb(ll *indexes, ll s, ll rest, function<void(ll *)> f) {
  if (rest == 0) {
    f(indexes);
  } else {
    if (s < 0)
      return;
    recursive_comb(indexes, s - 1, rest, f);
    indexes[rest - 1] = s;
    recursive_comb(indexes, s - 1, rest - 1, f);
  }
}

// nCkの組み合わせに対して処理を実行する
void foreach_comb(ll n, ll k, function<void(ll *)> f) {
  ll indexes[k];
  recursive_comb(indexes, n - 1, k, f);
}

// nPkの順列に対して処理を実行する
void foreach_permutation(ll n, ll k, function<void(ll *)> f) {
  foreach_comb(n, k, [&](ll *c_indexes) {
    foreach_permutation(k, [&](ll *p_indexes) {
      ll indexes[k];
      for (ll i = 0; i < k; i++) {
        indexes[i] = c_indexes[p_indexes[i]];
      }
      f(indexes);
    });
  });
}

// ll arr[1000500];
// vint primes;

// //エラトステネスの篩
// void Eratosthenes(){
//   ll N = 1000500;
// 	for(ll i = 0; i < N; i++){
// 		arr[i] = 1;
// 	}
// 	for(ll i = 2; i < sqrt(N); i++){
// 		if(arr[i]){
// 			for(ll j = 0; i * (j + 2) < N; j++){
// 				arr[i *(j + 2)] = 0;
// 			}
// 		}
// 	}

// 	for(ll i = 2; i < N; i++){
// 		if(arr[i]){
//       primes.pb(i);
// 			//cout << i << endl;
// 		}
// 	}
// }

void print(vint &V) {
  for (auto e : V)
    cout << e << " ";
  cout << endl;
}

int main() {
  cout << fixed << setprecision(12);

  ll N;
  cin >> N;
  vint D(N);
  rep(i, N) cin >> D[i];

  vint cnt(N, 0);
  rep(i, N) { cnt[D[i]]++; }

  if (D[0] > 0 || cnt[0] > 1) {
    cout << 0 << endl;
    return 0;
  }

  ll ans = 1;
  ll maxval = *max_element(ALL(D));
  rep(i, maxval) {
    if (cnt[i] == 0) {
      cout << 0 << endl;
      return 0;
    }
    ans *= power(cnt[i], cnt[i + 1]);
    ans %= MOD;
  }

  cout << ans << endl;
}