#include <bits/stdc++.h>
#define REP(i, l, r) for (int i = (l); i <= (r); ++ i)
#define DEP(i, r, l) for (int i = (r); i >= (l); -- i)
#define fi first
#define se second
#define pb emplace_back
#define mems(x, v) memset((x), (v), sizeof(x))
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(), (x).end()
using namespace std;
namespace Milkcat {
	typedef long double LD;
	typedef pair<int, int> pii;
	const int N = 1e5 + 5, M = 405;
	const LD eps = 1E-16;
	int n, m, p[M], q[M]; LD f[N][3],  ge[M][M * 2], eq[M][M * 2];
	void chkmax(LD &x, LD y) { x = max(x, y); }
	int main() {
		cin >> n, m = 333;
		REP(i, 1, n) cin >> p[i];
		REP(i, 1, n) cin >> q[i];
		REP(i, 1, m) REP(j, 0, m * 2) {
			REP(x, 1, i) {
				ge[i][j] += min(x, j + 1);
				eq[i][j] += (x <= j);
			}
			ge[i][j] /= i * (j + 1), eq[i][j] /= i * (j + 1);
		}
		DEP(i, n, 1) REP(j, 1, p[i]) {
			if (i + j > n + 1) break;
			chkmax(f[i][0], 1 - f[i + j][1]);
			chkmax(f[i][1], 1 - f[i + j][1]);
			chkmax(f[i][2], f[i + j][1]);
			int x = p[i] - j, y = q[i] + q[i + j];
			if (x > 0) chkmax(f[i][1], f[i + j][0] * ge[x][y] + (1 - f[i + j][1]) * eq[x][y] + (1 - f[i + j][2]) * (1 - ge[x][y] - eq[x][y]));
		}
		cout << fixed << setprecision(10) << f[1][1] << '\n';
		return 0;
	}
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
	int T = 1;
	while (T --) Milkcat::main();
	return 0;
}