import sys
input = sys.stdin.readline
from heapq import *
INF=1<<60
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
M=[]
mx=-INF
for i in range(N):
    if A[i]>B[i]:A[i],B[i]=B[i],A[i]
    M.append(A[i]+B[i]>>1)
heap=[]
for i,a in enumerate(A):
    heappush(heap, (a,i))
    mx = max(mx,a)
ans=mx-heap[0][0]
while True:
    x,i = heappop(heap)
    if x==B[i]:break
    if x==M[i]:
        b=B[i]
        heappush(heap, (b,i))
        mx = max(mx,b)
    else:
        m = M[i]
        heappush(heap, (m,i))
        mx = max(mx,m)
    ans = min(ans, mx-heap[0][0])

print(ans)