import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

def main():
    # 区間[l,r)でiが優勝する確率
    def pwin(l, r, i):
        if (l, r, i) in memo: return memo[l, r, i]
        if r - l == 1: return 1
        m = (l + r) // 2
        res = 0
        si = ss[i]
        if i < m:
            for j in range(m, r):
                sj = ss[j]
                res += pwin(m, r, j) * si ** 2 / (si ** 2 + sj ** 2)
            res *= pwin(l, m, i)
        else:
            for j in range(l, m):
                sj = ss[j]
                res += pwin(l, m, j) * si ** 2 / (si ** 2 + sj ** 2)
            res *= pwin(m, r, i)
        memo[l, r, i] = res
        return res

    memo = {}

    m = II()
    n = 1 << m
    ss = [II() for _ in range(n)]
    print(pwin(0, n, 0))

main()