#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
	int i, N, A[100001];
	long double p[100001], q[100001];
	scanf("%d", &N);
	for (i = 1; i <= N; i++) scanf("%Lf", &(p[i]));
	for (i = 1; i <= N; i++) scanf("%Lf", &(q[i]));
	for (i = 1; i <= N; i++) scanf("%d", &(A[i]));
	
	int flag = 1;
	long double x[100001], y[100001], sum, tmp;
	for (i = 1; i <= N; i++) x[i] = 0.5;
	while (flag == 1) {
		flag = 0;
		for (i = 1, sum = 0.0; i <= N; i++) sum += p[i] * x[i];
		for (i = 1; i <= N; i++) {
			tmp = 1.0 - q[i] * (sum - p[i] * x[i]);
			y[i] = (tmp - sqrtl(tmp * tmp - 4 * q[i] * (1.0 - q[i]) * p[i])) / (2.0 * q[i] * p[i]);
			if (fabsl(y[i] - x[i]) > 1e-10) flag = 1;
		}
		for (i = 1; i <= N; i++) x[i] = (x[i] + y[i]) / 2.0;
	}
	
	long double ans = 0.0;
	for (i = 1; i <= N; i++) ans += logl(x[i]) * A[i];
	printf("%.7Lf\n", ans);
	fflush(stdout);
	return 0;
}