import heapq
N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C = []
mi_max = 10**9
for i in range(N):
    if A[i]>B[i]:
        A[i],B[i]=B[i],A[i]
    C.append([A[i],(A[i]+B[i])//2,B[i]])
    mi_max = min(mi_max,B[i])
mi = 10**9
ma = 0
h = []
for i,a in enumerate(A):
    mi = min(mi,a)
    ma = max(ma,a)
    heapq.heappush(h,(a,i,0))
ans = ma-mi
while h:
    before,i,ii= heapq.heappop(h)
    if ii==0:
        heapq.heappush(h,((A[i]+B[i])//2,i,1))
        ma = max(ma,(A[i]+B[i])//2)
    if ii==1:
        ma = max(ma,B[i])
    if len(h):
        mi=min(h[0][0],mi_max)
    ans = min(ans,ma-mi)
print(ans)