#include <bits/stdc++.h>
const int P = 998244353;
inline int mul(const int &a, const int &b) { return 1ll * a * b % P; }
inline int add(int a, const int &b) {
  a += b;
  return (a >= P) ? a - P : a;
}
inline int sub(int a, const int &b) {
  a -= b;
  return (a < 0) ? a + P : a;
}
int qsm(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = mul(ans, a);
    a = mul(a, a);
    b >>= 1;
  }
  return ans;
}
int C[41][41], inv[41];
int gcd(int a, int b) { return (!b) ? a : gcd(b, a % b); }
struct fract {
  int a, b;
  fract operator+(int n) { return (fract){a + b * n, b}; }
  bool operator>=(const fract &rhs) const {
    return 1ll * a * rhs.b >= 1ll * b * rhs.a;
  }
  bool operator==(const fract &rhs) const {
    return 1ll * a * rhs.b == 1ll * b * rhs.a;
  }
  bool operator<(const fract &rhs) const {
    return 1ll * a * rhs.b < 1ll * b * rhs.a;
  }
} x[31];
struct interval {
  fract l;
  std::vector<int> f;
};
std::vector<interval> vec, vec2;
std::vector<fract> cut;
std::vector<int> h[100001], tem[100001];
int n;
fract read() {
  fract x;
  int y = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') ch = getchar();
  while (ch != '.' && ch != '\n') y = y * 10 + ch - '0', ch = getchar();
  if (ch == '\n') return (fract){y, 1};
  x.a = 0, x.b = 1;
  ch = getchar();
  while (ch >= '0' && ch <= '9')
    x.a = x.a * 10 + ch - '0', x.b *= 10, ch = getchar();
  int _gcd = gcd(x.a, x.b);
  x.a /= _gcd, x.b /= _gcd;
  x = x + y;
  return x;
}
std::vector<int> operator+=(std::vector<int> &a, std::vector<int> b) {
  if ((int)a.size() < (int)b.size()) a.resize((int)b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] = add(a[i], b[i]);
  return a;
}
std::vector<int> operator-=(std::vector<int> &a, std::vector<int> b) {
  if ((int)a.size() < (int)b.size()) a.resize((int)b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] = sub(a[i], b[i]);
  return a;
}
std::vector<int> operator*(std::vector<int> a, std::vector<int> b) {
  std::vector<int> c((int)a.size() + (int)b.size() - 1);
  for (int i = 0; i < (int)a.size(); i++)
    for (int j = 0; j < (int)b.size(); j++)
      c[i + j] = add(c[i + j], mul(a[i], b[j]));
  return c;
}
std::vector<int> trans(std::vector<int> a) {
  std::vector<int> b((int)a.size());
  for (int i = 0; i < (int)a.size(); i++)
    for (int j = 0; j <= i; j++)
      b[j] = (((i - j) & 1) ? sub : add)(b[j], mul(C[i][j], a[i]));
  return b;
}
std::vector<int> trans2(std::vector<int> a) {
  std::vector<int> b((int)a.size() + 1);
  for (int i = 0; i < (int)a.size(); i++)
    b[i + 1] = mul(a[i], mul(i, inv[i + 1]));
  return b;
}
int eval(std::vector<int> a, fract x) {
  int n = mul(x.a, qsm(x.b, P - 2));
  int tot = 0;
  for (int i = 0, Mul = 1; i < (int)a.size(); i++, Mul = mul(Mul, n))
    tot = add(tot, mul(Mul, a[i]));
  return tot;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i <= 40; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++) C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]);
  }
  inv[0] = inv[1] = 1;
  for (int i = 2; i <= 40; i++) inv[i] = mul(P - P / i, inv[P % i]);
  for (int i = 1; i <= n; i++) x[i] = read();
  vec.push_back((interval){(fract){0, 1}, std::vector<int>(1, 1)});
  std::vector<int> x, b;
  x.push_back(0);
  x.push_back(1);
  b.push_back(P - 1);
  b.push_back(1);
  for (int fd = 1; fd <= n; fd++) {
    cut.clear();
    for (int i = 0; i < (int)vec.size(); i++)
      cut.push_back(vec[i].l), cut.push_back(vec[i].l + 1);
    std::sort(cut.begin(), cut.end());
    cut.resize(std::unique(cut.begin(), cut.end()) - cut.begin());
    for (int i = 0; i < (int)vec.size(); i++) {
      tem[i] = trans2(vec[i].f);
    }
    for (int i = 0; i < (int)vec.size() - 1; i++) {
      h[i].resize(2);
      h[i][1] = sub(eval(vec[i].f, vec[i + 1].l), eval(vec[i].f, vec[i].l));
      h[i][0] = sub(eval(tem[i], vec[i].l), eval(tem[i], vec[i + 1].l));
    }
    for (int i = 0, j = -1, k = 0; i < (int)cut.size(); i++) {
      while (k < (int)vec.size() - 1 && cut[i] >= vec[k + 1].l) ++k;
      while (j < (int)vec.size() - 1 && cut[i] >= vec[j + 1].l + 1) ++j;
      vec2.push_back((interval){cut[i], std::vector<int>()});
      if (~j) vec2.back().f += trans(vec[j].f);
      for (int l = j + 1; l < k; l++) vec2.back().f += h[l];
      vec2.back().f += x * vec[k].f;
      vec2.back().f[1] = sub(vec2.back().f[1], eval(vec[k].f, vec[k].l));
      vec2.back().f -= tem[k];
      vec2.back().f[0] = add(vec2.back().f[0], eval(tem[k], vec[k].l));
      if (~j) {
        vec2.back().f -= x * trans(vec[j].f);
        vec2.back().f[1] = add(vec2.back().f[1], eval(vec[j].f, vec[j + 1].l));
        vec2.back().f += trans(tem[j]);
        vec2.back().f[0] = sub(vec2.back().f[0], eval(tem[j], vec[j + 1].l));
      }
      if (fd == 1 && cut[i] == (fract){0, 1}) vec2.back().f += x;
    }
    while (::x[fd] < cut.back()) cut.pop_back(), vec2.pop_back();
    int v = eval(vec2.back().f, ::x[fd]);
    if (::x[fd] == cut.back()) cut.pop_back(), vec2.pop_back();
    vec2.push_back((interval){::x[fd], std::vector<int>(1, v)});
    vec = vec2;
    vec2.clear();
  }
  printf("%d\n", vec.back().f[0]);
}

### Prompt

Construct a CPP code solution to the problem outlined:

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.

### Response

```cpp
#include <bits/stdc++.h>
const int P = 998244353;
inline int mul(const int &a, const int &b) { return 1ll * a * b % P; }
inline int add(int a, const int &b) {
  a += b;
  return (a >= P) ? a - P : a;
}
inline int sub(int a, const int &b) {
  a -= b;
  return (a < 0) ? a + P : a;
}
int qsm(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = mul(ans, a);
    a = mul(a, a);
    b >>= 1;
  }
  return ans;
}
int C[41][41], inv[41];
int gcd(int a, int b) { return (!b) ? a : gcd(b, a % b); }
struct fract {
  int a, b;
  fract operator+(int n) { return (fract){a + b * n, b}; }
  bool operator>=(const fract &rhs) const {
    return 1ll * a * rhs.b >= 1ll * b * rhs.a;
  }
  bool operator==(const fract &rhs) const {
    return 1ll * a * rhs.b == 1ll * b * rhs.a;
  }
  bool operator<(const fract &rhs) const {
    return 1ll * a * rhs.b < 1ll * b * rhs.a;
  }
} x[31];
struct interval {
  fract l;
  std::vector<int> f;
};
std::vector<interval> vec, vec2;
std::vector<fract> cut;
std::vector<int> h[100001], tem[100001];
int n;
fract read() {
  fract x;
  int y = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') ch = getchar();
  while (ch != '.' && ch != '\n') y = y * 10 + ch - '0', ch = getchar();
  if (ch == '\n') return (fract){y, 1};
  x.a = 0, x.b = 1;
  ch = getchar();
  while (ch >= '0' && ch <= '9')
    x.a = x.a * 10 + ch - '0', x.b *= 10, ch = getchar();
  int _gcd = gcd(x.a, x.b);
  x.a /= _gcd, x.b /= _gcd;
  x = x + y;
  return x;
}
std::vector<int> operator+=(std::vector<int> &a, std::vector<int> b) {
  if ((int)a.size() < (int)b.size()) a.resize((int)b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] = add(a[i], b[i]);
  return a;
}
std::vector<int> operator-=(std::vector<int> &a, std::vector<int> b) {
  if ((int)a.size() < (int)b.size()) a.resize((int)b.size());
  for (int i = 0; i < (int)b.size(); i++) a[i] = sub(a[i], b[i]);
  return a;
}
std::vector<int> operator*(std::vector<int> a, std::vector<int> b) {
  std::vector<int> c((int)a.size() + (int)b.size() - 1);
  for (int i = 0; i < (int)a.size(); i++)
    for (int j = 0; j < (int)b.size(); j++)
      c[i + j] = add(c[i + j], mul(a[i], b[j]));
  return c;
}
std::vector<int> trans(std::vector<int> a) {
  std::vector<int> b((int)a.size());
  for (int i = 0; i < (int)a.size(); i++)
    for (int j = 0; j <= i; j++)
      b[j] = (((i - j) & 1) ? sub : add)(b[j], mul(C[i][j], a[i]));
  return b;
}
std::vector<int> trans2(std::vector<int> a) {
  std::vector<int> b((int)a.size() + 1);
  for (int i = 0; i < (int)a.size(); i++)
    b[i + 1] = mul(a[i], mul(i, inv[i + 1]));
  return b;
}
int eval(std::vector<int> a, fract x) {
  int n = mul(x.a, qsm(x.b, P - 2));
  int tot = 0;
  for (int i = 0, Mul = 1; i < (int)a.size(); i++, Mul = mul(Mul, n))
    tot = add(tot, mul(Mul, a[i]));
  return tot;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i <= 40; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++) C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]);
  }
  inv[0] = inv[1] = 1;
  for (int i = 2; i <= 40; i++) inv[i] = mul(P - P / i, inv[P % i]);
  for (int i = 1; i <= n; i++) x[i] = read();
  vec.push_back((interval){(fract){0, 1}, std::vector<int>(1, 1)});
  std::vector<int> x, b;
  x.push_back(0);
  x.push_back(1);
  b.push_back(P - 1);
  b.push_back(1);
  for (int fd = 1; fd <= n; fd++) {
    cut.clear();
    for (int i = 0; i < (int)vec.size(); i++)
      cut.push_back(vec[i].l), cut.push_back(vec[i].l + 1);
    std::sort(cut.begin(), cut.end());
    cut.resize(std::unique(cut.begin(), cut.end()) - cut.begin());
    for (int i = 0; i < (int)vec.size(); i++) {
      tem[i] = trans2(vec[i].f);
    }
    for (int i = 0; i < (int)vec.size() - 1; i++) {
      h[i].resize(2);
      h[i][1] = sub(eval(vec[i].f, vec[i + 1].l), eval(vec[i].f, vec[i].l));
      h[i][0] = sub(eval(tem[i], vec[i].l), eval(tem[i], vec[i + 1].l));
    }
    for (int i = 0, j = -1, k = 0; i < (int)cut.size(); i++) {
      while (k < (int)vec.size() - 1 && cut[i] >= vec[k + 1].l) ++k;
      while (j < (int)vec.size() - 1 && cut[i] >= vec[j + 1].l + 1) ++j;
      vec2.push_back((interval){cut[i], std::vector<int>()});
      if (~j) vec2.back().f += trans(vec[j].f);
      for (int l = j + 1; l < k; l++) vec2.back().f += h[l];
      vec2.back().f += x * vec[k].f;
      vec2.back().f[1] = sub(vec2.back().f[1], eval(vec[k].f, vec[k].l));
      vec2.back().f -= tem[k];
      vec2.back().f[0] = add(vec2.back().f[0], eval(tem[k], vec[k].l));
      if (~j) {
        vec2.back().f -= x * trans(vec[j].f);
        vec2.back().f[1] = add(vec2.back().f[1], eval(vec[j].f, vec[j + 1].l));
        vec2.back().f += trans(tem[j]);
        vec2.back().f[0] = sub(vec2.back().f[0], eval(tem[j], vec[j + 1].l));
      }
      if (fd == 1 && cut[i] == (fract){0, 1}) vec2.back().f += x;
    }
    while (::x[fd] < cut.back()) cut.pop_back(), vec2.pop_back();
    int v = eval(vec2.back().f, ::x[fd]);
    if (::x[fd] == cut.back()) cut.pop_back(), vec2.pop_back();
    vec2.push_back((interval){::x[fd], std::vector<int>(1, v)});
    vec = vec2;
    vec2.clear();
  }
  printf("%d\n", vec.back().f[0]);
}

```