N = int(input())
A = list(map(float,input().split()))
B = list(map(float,input().split()))

def check(n):
    MIN = 1e9
    S = [v:=0.0] + [v:=v+A[i]-n*B[i] for i in range(N)]
    v = 1e18
    MIN_left = [v:=min(v,S[i]) for i in range(N)]
    v = -1e18
    MAX_right = [v:=max(v,S[i]) for i in range(N,-1,-1)][::-1]
    for i in range(N):
        MIN = min(MIN, MAX_right[i+1] - MIN_left[i])
    return MIN > 0.0

ok,ng = 0.0, 1e9
while(ng - ok > 1e-7):
    mid = (ok+ng)/2
    if(check(mid)):
        ok = mid
    else:
        ng = mid
print(ok)