#include <stdio.h>
 
#define maxn 2222
 
double prob[maxn][maxn];
int i, j;
 
void init() {
   /*
    * prob[i][j] represents the probability that alice picks jth element if there are i elements in total.
    * Take 1, 2, 3, 4
    * In the next move we can reach A -> 1, 2, 3 or B -> 2, 3, 4
    * hence prob[i][j] = 1 - 0.5 * ( prob[i-1][j] {this denotes A} + prob[i-1][j-1] { we get an offset of 1 look at B} )
    * As we have noticed this depends only on N and the position not on the actual value present at that position. Hence we can precompute for all N.
    */
    for(i=1; i < maxn; i++) {
        for(j = 1; j<= i;j++) {
            prob[i][j] = 1.0 - 0.5 * (prob[i-1][j] + prob[i-1][j-1]);
        }
    }
    return;
}
 
int a[maxn];
 
int main() {
    int nt, n;
    init();
    scanf("%d",&nt);
    while(nt--) {
        double ans = 0.0;
        scanf("%d",&n);
        for(i=1; i<=n; i++)
            scanf("%d",&a[i]);
        for(i=1;i<=n;i++)
            ans += prob[n][i] * a[i];
        printf("%.6lf\n",ans);
    }
    return 0;
}