import sys

# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()

dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
# md = 10**9+7
md = 998244353

from collections import deque
from heapq import *

n = II()
aa = LI()
bb = LI()

for i in range(n):
    if aa[i] > bb[i]:
        aa[i], bb[i] = bb[i], aa[i]

hp = []
mx = -inf
for i, a in enumerate(aa):
    heappush(hp, (a, i))
    mx = max(mx, a)

ans = mx-hp[0][0]
while 1:
    a, i = heappop(hp)
    if a == bb[i]: break
    if a == (aa[i]+bb[i])//2:
        heappush(hp, (bb[i], i))
        mx = max(mx, bb[i])
    elif a == aa[i]:
        c = (aa[i]+bb[i])//2
        heappush(hp, (c, i))
        mx = max(mx, c)
    ans = min(ans, mx-hp[0][0])

print(ans)