#include <bits/stdc++.h>
using namespace std;
const int maxn = 34;
const int ex = 1000000;
constexpr int mdn = 998244353;
struct mint {
  int v;
  inline operator int() const { return v; }
  inline mint(int v = 0) : v(v) {}
  inline bool operator==(const mint& a) const { return v == a.v; }
  inline bool operator!=(const mint& a) const { return v != a.v; }
  inline mint operator~() const {
    int r = 1, b = v;
    for (int i = 1; i <= (mdn - 2); i <<= 1) {
      if ((mdn - 2) & i) r = r * (long long)b % mdn;
      b = b * (long long)b % mdn;
    }
    return mint(r);
  }
  inline mint operator-() const { return mint(v ? mdn - v : 0); }
  inline mint operator+(const mint& a) const {
    mint c(v + a.v);
    if (c.v >= mdn) c.v -= mdn;
    return c;
  }
  inline mint operator-(const mint& a) const {
    mint c(v - a.v);
    if (c.v < 0) c.v += mdn;
    return c;
  }
  inline mint operator*(const mint& a) const {
    return mint(v * (long long)a.v % mdn);
  }
  inline mint operator/(const mint& a) const { return (*this) * ~a; }
  inline mint& operator++() {
    v++;
    if (v == mdn) v = 0;
    return *this;
  }
  inline mint& operator--() {
    v--;
    if (v == -1) v = mdn - 1;
    return *this;
  }
  inline mint operator++(int) {
    mint ret = *this;
    ++*this;
    return ret;
  }
  inline mint operator--(int) {
    mint ret = *this;
    ++*this;
    return ret;
  }
  inline mint& operator+=(const mint& a) {
    v += a.v;
    if (v >= mdn) v -= mdn;
    return *this;
  }
  inline mint& operator-=(const mint& a) {
    v -= a.v;
    if (v < 0) v += mdn;
    return *this;
  }
  inline mint& operator*=(const mint& a) {
    v = v * (long long)a.v % mdn;
    return *this;
  }
  inline mint& operator/=(const mint& a) {
    v = v * (long long)(~a).v % mdn;
    return *this;
  }
  friend istream& operator>>(istream& s, mint& a) {
    s >> a.v;
    return s;
  }
  friend ostream& operator<<(ostream& s, const mint& a) {
    s << a.v;
    return s;
  }
};
mint inv[maxn];
vector<mint> integ(vector<mint> x) {
  x.push_back(0);
  for (int i = x.size() - 1; i > 0; i--) x[i] = x[i - 1];
  x[0] = 0;
  for (int i = 1; i < x.size(); i++) x[i] = x[i] * inv[i] % mdn;
  return x;
}
mint calc(vector<mint> x, mint val) {
  mint ans;
  for (int i = x.size() - 1; i >= 0; i--) ans = ans * val + x[i];
  return ans;
}
vector<mint> add(vector<mint> a, vector<mint> b) {
  if (a.size() < b.size()) swap(a, b);
  for (int i = 0; i < b.size(); i++) a[i] += b[i];
  return a;
}
vector<mint> sub(vector<mint> a, vector<mint> b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < b.size(); i++) a[i] -= b[i];
  return a;
}
mint binom[maxn][maxn];
vector<mint> plg(vector<mint> a, mint dlt) {
  vector<mint> ret;
  ret.resize(a.size());
  for (int i = 0; i < a.size(); i++) {
    mint pw = 1;
    for (int j = i; j >= 0; j--) {
      ret[j] += a[i] * binom[i][j] * pw;
      pw *= dlt;
    }
  }
  return ret;
}
int n;
int p[maxn];
vector<mint> dp[maxn][maxn * maxn];
mint pfx[maxn * maxn];
vector<int> pt;
vector<int> prv;
int main() {
  for (int i = 0; i < maxn; i++) {
    binom[i][0] = 1;
    for (int j = 1; j <= i; j++)
      binom[i][j] = binom[i - 1][j] + binom[i - 1][j - 1];
  }
  for (int i = 1; i < maxn; i++) inv[i] = ~(mint)i;
  mint invex = ~(mint)ex;
  cin >> n;
  pt.push_back(0);
  for (int i = 0; i <= n; i++) pt.push_back(i * ex);
  for (int i = 1; i <= n; i++) {
    double t;
    cin >> t;
    p[i] = (int)(t * ex + 0.5);
    for (int j = 0; j <= n; j++) {
      pt.push_back(p[i] % ex + j * ex);
    }
  }
  sort(pt.begin(), pt.end());
  pt.resize(unique(pt.begin(), pt.end()) - pt.begin());
  prv.resize(pt.size());
  for (int i = 0; i < pt.size(); i++) {
    prv[i] = -1;
    for (int j = 0; j < pt.size(); j++) {
      if (pt[j] == pt[i] - ex) prv[i] = j;
    }
  }
  for (int i = 1; i < pt.size(); i++) {
    dp[1][i] = {invex};
    if (pt[i] == ex || pt[i] == p[1]) break;
  }
  for (int i = 2; i <= n; i++) {
    for (int j = 1; j < pt.size(); j++) {
      int l = pt[j - 1], r = pt[j];
      dp[i - 1][j] = integ(dp[i - 1][j]);
      pfx[j] = pfx[j - 1] + calc(dp[i - 1][j], r) - calc(dp[i - 1][j], l);
      dp[i][j] = dp[i - 1][j];
      dp[i][j][0] -= calc(dp[i - 1][j], l);
      dp[i][j][0] += pfx[j - 1];
      if (prv[j] >= 0) dp[i][j][0] -= pfx[prv[j]];
      if (prv[j - 1] >= 0) {
        int pr = prv[j];
        dp[i][j] = sub(dp[i][j], plg(dp[i - 1][pr], mdn - ex));
        dp[i][j][0] += calc(dp[i - 1][pr], pt[pr]);
      }
      for (int k = 0; k < dp[i][j].size(); k++) dp[i][j][k] *= invex;
      if (pt[j] == p[i]) break;
    }
  }
  mint ans = 0;
  for (int j = 1; j < pt.size(); j++) {
    vector<mint> ig = integ(dp[n][j]);
    ans += calc(ig, pt[j]) - calc(ig, pt[j - 1]);
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Generate a Cpp solution to the following 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 34;
const int ex = 1000000;
constexpr int mdn = 998244353;
struct mint {
  int v;
  inline operator int() const { return v; }
  inline mint(int v = 0) : v(v) {}
  inline bool operator==(const mint& a) const { return v == a.v; }
  inline bool operator!=(const mint& a) const { return v != a.v; }
  inline mint operator~() const {
    int r = 1, b = v;
    for (int i = 1; i <= (mdn - 2); i <<= 1) {
      if ((mdn - 2) & i) r = r * (long long)b % mdn;
      b = b * (long long)b % mdn;
    }
    return mint(r);
  }
  inline mint operator-() const { return mint(v ? mdn - v : 0); }
  inline mint operator+(const mint& a) const {
    mint c(v + a.v);
    if (c.v >= mdn) c.v -= mdn;
    return c;
  }
  inline mint operator-(const mint& a) const {
    mint c(v - a.v);
    if (c.v < 0) c.v += mdn;
    return c;
  }
  inline mint operator*(const mint& a) const {
    return mint(v * (long long)a.v % mdn);
  }
  inline mint operator/(const mint& a) const { return (*this) * ~a; }
  inline mint& operator++() {
    v++;
    if (v == mdn) v = 0;
    return *this;
  }
  inline mint& operator--() {
    v--;
    if (v == -1) v = mdn - 1;
    return *this;
  }
  inline mint operator++(int) {
    mint ret = *this;
    ++*this;
    return ret;
  }
  inline mint operator--(int) {
    mint ret = *this;
    ++*this;
    return ret;
  }
  inline mint& operator+=(const mint& a) {
    v += a.v;
    if (v >= mdn) v -= mdn;
    return *this;
  }
  inline mint& operator-=(const mint& a) {
    v -= a.v;
    if (v < 0) v += mdn;
    return *this;
  }
  inline mint& operator*=(const mint& a) {
    v = v * (long long)a.v % mdn;
    return *this;
  }
  inline mint& operator/=(const mint& a) {
    v = v * (long long)(~a).v % mdn;
    return *this;
  }
  friend istream& operator>>(istream& s, mint& a) {
    s >> a.v;
    return s;
  }
  friend ostream& operator<<(ostream& s, const mint& a) {
    s << a.v;
    return s;
  }
};
mint inv[maxn];
vector<mint> integ(vector<mint> x) {
  x.push_back(0);
  for (int i = x.size() - 1; i > 0; i--) x[i] = x[i - 1];
  x[0] = 0;
  for (int i = 1; i < x.size(); i++) x[i] = x[i] * inv[i] % mdn;
  return x;
}
mint calc(vector<mint> x, mint val) {
  mint ans;
  for (int i = x.size() - 1; i >= 0; i--) ans = ans * val + x[i];
  return ans;
}
vector<mint> add(vector<mint> a, vector<mint> b) {
  if (a.size() < b.size()) swap(a, b);
  for (int i = 0; i < b.size(); i++) a[i] += b[i];
  return a;
}
vector<mint> sub(vector<mint> a, vector<mint> b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < b.size(); i++) a[i] -= b[i];
  return a;
}
mint binom[maxn][maxn];
vector<mint> plg(vector<mint> a, mint dlt) {
  vector<mint> ret;
  ret.resize(a.size());
  for (int i = 0; i < a.size(); i++) {
    mint pw = 1;
    for (int j = i; j >= 0; j--) {
      ret[j] += a[i] * binom[i][j] * pw;
      pw *= dlt;
    }
  }
  return ret;
}
int n;
int p[maxn];
vector<mint> dp[maxn][maxn * maxn];
mint pfx[maxn * maxn];
vector<int> pt;
vector<int> prv;
int main() {
  for (int i = 0; i < maxn; i++) {
    binom[i][0] = 1;
    for (int j = 1; j <= i; j++)
      binom[i][j] = binom[i - 1][j] + binom[i - 1][j - 1];
  }
  for (int i = 1; i < maxn; i++) inv[i] = ~(mint)i;
  mint invex = ~(mint)ex;
  cin >> n;
  pt.push_back(0);
  for (int i = 0; i <= n; i++) pt.push_back(i * ex);
  for (int i = 1; i <= n; i++) {
    double t;
    cin >> t;
    p[i] = (int)(t * ex + 0.5);
    for (int j = 0; j <= n; j++) {
      pt.push_back(p[i] % ex + j * ex);
    }
  }
  sort(pt.begin(), pt.end());
  pt.resize(unique(pt.begin(), pt.end()) - pt.begin());
  prv.resize(pt.size());
  for (int i = 0; i < pt.size(); i++) {
    prv[i] = -1;
    for (int j = 0; j < pt.size(); j++) {
      if (pt[j] == pt[i] - ex) prv[i] = j;
    }
  }
  for (int i = 1; i < pt.size(); i++) {
    dp[1][i] = {invex};
    if (pt[i] == ex || pt[i] == p[1]) break;
  }
  for (int i = 2; i <= n; i++) {
    for (int j = 1; j < pt.size(); j++) {
      int l = pt[j - 1], r = pt[j];
      dp[i - 1][j] = integ(dp[i - 1][j]);
      pfx[j] = pfx[j - 1] + calc(dp[i - 1][j], r) - calc(dp[i - 1][j], l);
      dp[i][j] = dp[i - 1][j];
      dp[i][j][0] -= calc(dp[i - 1][j], l);
      dp[i][j][0] += pfx[j - 1];
      if (prv[j] >= 0) dp[i][j][0] -= pfx[prv[j]];
      if (prv[j - 1] >= 0) {
        int pr = prv[j];
        dp[i][j] = sub(dp[i][j], plg(dp[i - 1][pr], mdn - ex));
        dp[i][j][0] += calc(dp[i - 1][pr], pt[pr]);
      }
      for (int k = 0; k < dp[i][j].size(); k++) dp[i][j][k] *= invex;
      if (pt[j] == p[i]) break;
    }
  }
  mint ans = 0;
  for (int j = 1; j < pt.size(); j++) {
    vector<mint> ig = integ(dp[n][j]);
    ans += calc(ig, pt[j]) - calc(ig, pt[j - 1]);
  }
  cout << ans << endl;
  return 0;
}

```