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

pq = []
for i in range(N):
    if A[i] > B[i]: A[i],B[i]=B[i],A[i]
    pq.append([A[i], i, 0])

from heapq import *
hi = max(x for x,i,j in pq)
heapify(pq)
ans = hi - pq[0][0]
while pq:
    x,i,j = heappop(pq)
    if j == 2:
        break
    if j == 0:
        x = A[i] + B[i] >> 1
        hi = max(hi, x)
        heappush(pq, [x,i,j+1])
    if j == 1:
        x = B[i]
        hi = max(hi, x)
        heappush(pq, [x,i,j+1])
    if pq:
        ans = min(ans, hi - pq[0][0])

print(ans)