You are given an integer x represented as a product of n its prime divisors p_1 ⋅ p_2, ⋅ … ⋅ p_n. Let S be the set of all positive integer divisors of x (including 1 and x itself).

We call a set of integers D good if (and only if) there is no pair a ∈ D, b ∈ D such that a ≠ b and a divides b.

Find a good subset of S with maximum possible size. Since the answer can be large, print the size of the subset modulo 998244353.

Input

The first line contains the single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of prime divisors in representation of x.

The second line contains n integers p_1, p_2, ..., p_n (2 ≤ p_i ≤ 3 ⋅ 10^6) — the prime factorization of x.

Output

Print the maximum possible size of a good subset modulo 998244353.

Examples

Input


3
2999999 43 2999957


Output


3


Input


6
2 3 2 3 2 2


Output


3

Note

In the first sample, x = 2999999 ⋅ 43 ⋅ 2999957 and one of the maximum good subsets is \{ 43, 2999957, 2999999 \}.

In the second sample, x = 2 ⋅ 3 ⋅ 2 ⋅ 3 ⋅ 2 ⋅ 2 = 144 and one of the maximum good subsets is \{ 9, 12, 16 \}.
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <int n, class... T>
typename std::enable_if<(n >= sizeof...(T))>::type __output_tuple(
    std::ostream &, std::tuple<T...> const &) {}
template <int n, class... T>
typename std::enable_if<(n < sizeof...(T))>::type __output_tuple(
    std::ostream &os, std::tuple<T...> const &t) {
  os << (n == 0 ? "" : ", ") << std::get<n>(t);
  __output_tuple<n + 1>(os, t);
}
template <class... T>
std::ostream &operator<<(std::ostream &os, std::tuple<T...> const &t) {
  os << "(";
  __output_tuple<0>(os, t);
  os << ")";
  return os;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::stack<T> &a) {
  os << "{";
  for (auto tmp = a; tmp.size(); tmp.pop())
    os << (a.size() == tmp.size() ? "" : ", ") << tmp.top();
  os << "}";
  return os;
}
template <class T, class Container, class Compare>
std::ostream &operator<<(std::ostream &os,
                         std::priority_queue<T, Container, Compare> a) {
  os << "{ (top) ";
  while (a.size()) os << a.top() << (a.size() == 1 ? "" : ", "), a.pop();
  os << " }";
  return os;
}
template <class T, class Container>
std::ostream &operator<<(std::ostream &os, std::queue<T, Container> a) {
  os << "{ ";
  while (a.size()) os << a.front() << (a.size() == 1 ? "" : ", "), a.pop();
  os << " }";
  return os;
}
template <
    class T,
    class = typename std::iterator_traits<decltype(begin(T()))>::value_type,
    class = typename std::enable_if<!std::is_same<T, std::string>::value>::type>
std::ostream &operator<<(std::ostream &os, const T &a) {
  for (auto ite = begin(a); ite != end(a); ++ite)
    os << (ite == begin(a) ? "" : " ") << *ite;
  return os;
}
namespace NTT {
using uint = uint_fast32_t;
constexpr ll NTT_PRIMES[][2] = {
    {1224736769, 3}, {1053818881, 7}, {1051721729, 6}, {1045430273, 3},
    {1012924417, 5}, {1007681537, 3}, {1004535809, 3}, {998244353, 3},
    {985661441, 3},  {976224257, 3},  {975175681, 17}, {962592769, 7},
    {950009857, 7},  {943718401, 7},  {935329793, 3},  {924844033, 5},
    {469762049, 3},  {167772161, 3},
};
ll extgcd(ll a, ll b, ll &x, ll &y) {
  ll d;
  return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
                : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
}
ll modinv(ll a, ll mod) {
  ll x, y;
  extgcd(a, mod, x, y);
  x %= mod;
  return x < 0 ? x + mod : x;
}
ll modpow(ll a, ll b, ll mod) {
  ll r = 1;
  a %= mod;
  while (b) {
    if (b & 1) r = r * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return r;
}
template <int MAX_H>
struct Pool {
  static ll *tmp, *A, *B;
};
template <int MAX_H>
ll *Pool<MAX_H>::tmp = new ll[1 << MAX_H];
template <int MAX_H>
ll *Pool<MAX_H>::A = new ll[1 << MAX_H];
template <int MAX_H>
ll *Pool<MAX_H>::B = new ll[1 << MAX_H];
template <int MAX_H, ll mod, ll primitive>
class Core {
 public:
  static_assert((mod & ((1 << MAX_H) - 1)) == 1,
                "mod is too small; comment out");
  ll zetaList[MAX_H], zetaInvList[MAX_H];
  Core() {
    zetaList[MAX_H - 1] = modpow(primitive, (mod - 1) / (1 << MAX_H), mod);
    zetaInvList[MAX_H - 1] = modinv(zetaList[MAX_H - 1], mod);
    for (int ih = MAX_H - 2; ih >= 0; --ih) {
      zetaList[ih] = zetaList[ih + 1] * zetaList[ih + 1] % mod;
      zetaInvList[ih] = zetaInvList[ih + 1] * zetaInvList[ih + 1] % mod;
    }
  }
  void fft(ll *a, uint n, uint nh, bool inverse) const {
    ll *tmp = Pool<MAX_H>::tmp;
    uint mask = n - 1;
    for (uint i = n >> 1, ih = nh - 1; i >= 1; i >>= 1, --ih) {
      ll zeta = inverse ? zetaInvList[nh - 1 - ih] : zetaList[nh - 1 - ih];
      ll powZeta = 1;
      for (uint j = 0; j < n; j += i) {
        for (uint k = 0; k < i; ++k) {
          tmp[j | k] = (a[((j << 1) & mask) | k] +
                        powZeta * a[(((j << 1) | i) & mask) | k]) %
                       mod;
        }
        powZeta = powZeta * zeta % mod;
      }
      swap(a, tmp);
    }
    if (nh & 1) {
      swap(a, tmp);
      for (uint i = 0; i < n; ++i) a[i] = tmp[i];
    }
    if (inverse) {
      ll invN = modinv(n, mod);
      for (uint i = 0; i < n; ++i) a[i] = a[i] * invN % mod;
    }
  }
  vector<ll> conv(const vector<ll> &a, const vector<ll> &b) const {
    uint t = a.size() + b.size() - 1;
    uint n = 1, nh = 0;
    while (n < t) n <<= 1, ++nh;
    return convStrict(a, b, n, nh);
  }
  vector<ll> convStrict(const vector<ll> &a, const vector<ll> &b, uint n,
                        uint nh) const {
    ll *A = Pool<MAX_H>::A, *B = Pool<MAX_H>::B;
    for (uint i = 0; i < n; ++i) A[i] = B[i] = 0;
    copy(a.begin(), a.end(), A);
    copy(b.begin(), b.end(), B);
    fft(A, n, nh, 0), fft(B, n, nh, 0);
    for (uint i = 0; i < n; ++i) A[i] = A[i] * B[i] % mod;
    fft(A, n, nh, 1);
    return vector<ll>(A, A + n);
  }
};
template <int MAX_H, int I>
class ConvolutionWithGarnerCore {
 public:
  static void conv_for(uint n, uint nh, const vector<ll> &a,
                       const vector<ll> &b, vector<ll> &mods,
                       vector<ll> &coeffs, vector<vector<ll> > &constants) {
    static const Core<MAX_H, NTT_PRIMES[I][0], NTT_PRIMES[I][1]> ntt;
    auto c = ntt.convStrict(a, b, n, nh);
    mods[I] = NTT_PRIMES[I][0];
    ConvolutionWithGarnerCore<MAX_H, I - 1>::conv_for(n, nh, a, b, mods, coeffs,
                                                      constants);
    for (size_t i = 0; i < c.size(); ++i) {
      ll v = (c[i] - constants[I][i]) * modinv(coeffs[I], mods[I]) % mods[I];
      if (v < 0) v += mods[I];
      for (size_t j = I + 1; j < mods.size(); ++j) {
        constants[j][i] = (constants[j][i] + coeffs[j] * v) % mods[j];
      }
    }
    for (size_t j = I + 1; j < mods.size(); ++j) {
      coeffs[j] = (coeffs[j] * mods[I]) % mods[j];
    }
  }
};
template <int MAX_H>
class ConvolutionWithGarnerCore<MAX_H, -1> {
 public:
  static void conv_for(uint, uint, const vector<ll> &, const vector<ll> &,
                       vector<ll> &, vector<ll> &, vector<vector<ll> > &) {}
};
template <int MAX_H>
class ConvolutionWithGarner {
 public:
  template <int USE>
  static vector<ll> conv(const vector<ll> &a, const vector<ll> &b, ll mod) {
    static_assert(USE >= 1, "USE must be positive");
    static_assert(USE <= sizeof(NTT_PRIMES) / sizeof(*NTT_PRIMES),
                  "USE is too big");
    uint nt = a.size() + b.size() - 1;
    uint n = 1, nh = 0;
    while (n < nt) n <<= 1, ++nh;
    vector<ll> coeffs(USE + 1, 1);
    vector<vector<ll> > constants(USE + 1, vector<ll>(n));
    vector<ll> mods(USE + 1, mod);
    ConvolutionWithGarnerCore<MAX_H, USE - 1>::conv_for(n, nh, a, b, mods,
                                                        coeffs, constants);
    return constants.back();
  }
};
}  // namespace NTT
NTT::Core<18, NTT::NTT_PRIMES[0][0], NTT::NTT_PRIMES[0][1]> nttBig;
NTT::Core<23, 998244353, 5> ntt;
using nttconv = NTT::ConvolutionWithGarner<18>;
constexpr int mod = 998244353;
constexpr int M = 3e6;
int cnt[M + 1];
int main() {
  std::ios::sync_with_stdio(false), std::cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    cnt[x]++;
  }
  n = 0;
  for (int i = 1; i < 10; i++) cnt[i] = i, n += i;
  using D = vector<ll>;
  using P = pair<int, D *>;
  priority_queue<P> vs;
  for (int i = 1; i <= M; i++)
    if (cnt[i]) vs.push(P(-(cnt[i] + 1), new D(cnt[i] + 1, 1)));
  while (vs.size() >= 2) {
    int x, y;
    D *u, *v;
    tie(x, u) = vs.top();
    vs.pop();
    tie(y, v) = vs.top();
    vs.pop();
    *u = ntt.conv(*u, *v);
    vs.push(P(-u->size(), u));
  }
  auto w = *(vs.top().second);
  ll ans = w[n / 2];
  cout << ans << endl;
  return 0;
}
