Problem: You generate real numbers s1, s2, ..., sn as follows: 

  * s0 = 0; 
  * si = si - 1 + ti, where ti is a real number chosen independently uniformly at random between 0 and 1, inclusive. 



You are given real numbers x1, x2, ..., xn. You are interested in the probability that si ≤ xi is true for all i simultaneously.

It can be shown that this can be represented as <image>, where P and Q are coprime integers, and <image>. Print the value of P·Q - 1 modulo 998244353.

Input

The first line contains integer n (1 ≤ n ≤ 30).

The next n lines contain real numbers x1, x2, ..., xn, given with at most six digits after the decimal point (0 < xi ≤ n).

Output

Print a single integer, the answer to the problem.

Examples

Input

4
1.00
2
3.000000
4.0


Output

1


Input

1
0.50216


Output

342677322


Input

2
0.5
1.0


Output

623902721


Input

6
0.77
1.234567
2.1
1.890
2.9999
3.77


Output

859831967

Note

In the first example, the sought probability is 1 since the sum of i real numbers which don't exceed 1 doesn't exceed i.

In the second example, the probability is x1 itself.

In the third example, the sought probability is 3 / 8.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular& operator/=(const Modular& other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = (int)998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
const int N = 40;
vector<vector<Mint>> C(N, vector<Mint>(N));
vector<Mint> p(N);
const int M = 1000000;
template <typename T>
void debug_out(T t) {
  cerr << t;
}
template <typename A, typename B>
void debug_out(pair<A, B> u) {
  cerr << "(" << u.first << " " << u.second << ")";
}
template <typename T>
void debug_out(vector<T> t) {
  int sz = t.size();
  for (int i = 0; i < sz; i++) {
    debug_out(t[i]);
    if (i != sz - 1) cerr << ", ";
  }
}
template <typename T>
void debug_out(vector<vector<T>> t) {
  int sz = t.size();
  for (int i = 0; i < sz; i++) {
    debug_out(t[i]);
    if (i != sz - 1) cerr << endl;
  }
}
struct poly {
  int n;
  vector<Mint> a;
  poly(){};
  poly(vector<Mint> _a) : a(_a) { n = a.size(); }
  Mint val(Mint x) {
    Mint cur = 1;
    Mint res = 0;
    for (int i = 0; i < n; i++) {
      res += cur * a[i];
      cur *= x;
    }
    return res;
  }
  poly sum() {
    vector<Mint> b = a;
    b.insert(b.begin(), 0);
    for (int i = 1; i < n + 1; i++) b[i] /= i;
    return poly(b);
  }
  poly shift() {
    vector<Mint> res(n);
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < i + 1; j++) {
        res[j] += a[i] * C[i][j] * p[i - j];
      }
    }
    return poly(res);
  }
  poly operator+(const poly& x) const {
    int sz = max(n, x.n);
    vector<Mint> l = a, r = x.a;
    l.resize(sz);
    r.resize(sz);
    for (int i = 0; i < sz; i++) l[i] += r[i];
    return poly(l);
  }
  poly operator-(const poly& x) const {
    int sz = max(n, x.n);
    vector<Mint> l = a, r = x.a;
    l.resize(sz);
    r.reserve(sz);
    for (int i = 0; i < sz; i++) l[i] -= r[i];
    return poly(l);
  }
};
void debug_out(poly a) { debug_out(a.a); }
int n;
struct upoly {
  int l, r;
  Mint sl, sr;
  poly c;
  poly sc;
  upoly(){};
  upoly(int _l, int _r, poly _c) : l(_l), r(_r), c(_c) {
    sc = c.sum();
    sl = sc.val(l);
    sr = sc.val(r);
  }
};
void debug_out(upoly a) {
  cerr << "(" << a.l << " " << a.r << "... ";
  debug_out(a.c);
  cerr << ")";
}
int main() {
  p[0] = 1;
  for (int i = 1; i < N; i++) p[i] = p[i - 1] * M;
  C[0][0] = 1;
  for (int i = 1; i < N; i++) {
    for (int j = 0; j < i + 1; j++) {
      C[i][j] = C[i - 1][j];
      if (j) C[i][j] += C[i - 1][j - 1];
    }
  }
  cin >> n;
  vector<int> p(n);
  for (int i = 0; i < n; i++) {
    double s;
    cin >> s;
    p[i] = s * M + 0.5;
  }
  reverse(p.begin(), p.end());
  vector<upoly> cur = {upoly(0, md - 1, poly((vector<Mint>){1}))};
  for (auto s : p) {
    while (cur.back().l >= s) cur.pop_back();
    cur.back().r = s;
    cur.back().sr = cur.back().sc.val(s);
    cur.push_back(upoly(s, md - 1, poly((vector<Mint>){0})));
    vector<upoly> bar;
    int sz = cur.size();
    int pos = 0, l = 0, r = 0;
    while (true) {
      while (l < sz && cur[l].r <= pos) {
        l++;
      }
      while (r < sz && cur[r].r <= pos + M) {
        r++;
      }
      if (r == sz) break;
      poly add = cur[r].sc.shift() - cur[l].sc;
      if (l != r) add.a[0] += cur[l].sr - cur[r].sl;
      for (int i = l + 1; i < r; i++) add.a[0] += cur[i].sr - cur[i].sl;
      for (auto& i : add.a) i /= M;
      int nxt = pos + min(cur[l].r - pos, cur[r].r - pos - M);
      bar.emplace_back(pos, nxt, add);
      pos = nxt;
    }
    swap(cur, bar);
    cur.back().r = md - 1;
  }
  cout << cur.front().c.val(0);
  return 0;
}