import sys
sys.setrecursionlimit(5*10**5)
input = sys.stdin.readline
from collections import defaultdict, deque, Counter
from heapq import heappop, heappush
from bisect import bisect_left, bisect_right
from math import gcd

n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = [(a[i]+b[i])//2 for i in range(n)]
all = [(a[i], i) for i in range(n)] +  [(b[i], i) for i in range(n)]  +  [(c[i], i) for i in range(n)] 
s = sorted(list(set(a + b + c)))


all.sort()

m = len(s)
r = 0
ll = 0
rr = 0
d = defaultdict(int)
now = 0
ans = float("inf")
for l in range(m):
    while r < m and now != n:
        while rr < 3*n and all[rr][0] == s[r]:
            d[all[rr][1]] += 1
            now += (d[all[rr][1]] == 1)
            rr += 1
        r += 1
    if now == n:
        ans = min(ans, s[r-1] - s[l])
    if now < n: break
    while ll < 3*n and all[ll][0] == s[l]:
        d[all[ll][1]] -= 1
        now -=(d[all[ll][1]] == 0)
        ll += 1
    

print(ans)