import sys

input = sys.stdin.buffer.readline


from heapq import heappop, heappush

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

bigpq = []
smallpq = []


# initialize
# a,b,half(a,b)の順に3*i, 3*i+1, 3*i+2のidxをふることにする
for i in range(n):
    a, b = A[i], B[i]
    if a > b:
        heappush(bigpq, (-b, 3 * i + 1))
        heappush(smallpq, (b, 3 * i + 1))
    else:
        heappush(bigpq, (-a, 3 * i))
        heappush(smallpq, (a, 3 * i))

cnt = [0] * n
ans = 1 << 100
finished = set()
while True:
    # print(ans)
    # print(smallpq)
    # print(bigpq)

    now_minimum, smallidx = heappop(smallpq)

    # smallidxのものはbiggestとして使えない
    finished.add(smallidx)
    # 使用済みbigpqだとアウト
    while bigpq:
        if bigpq[0][1] in finished:
            heappop(bigpq)
        else:
            break

    # 使える最大候補がない
    if not bigpq:
        break

    biggest, bigidx = bigpq[0]
    biggest *= -1

    ans = min(ans, biggest - now_minimum)
    biggest *= -1
    # smallidxと同じiのもので、次のものを追加する。
    idx = smallidx // 3
    cnt[idx] += 1
    a, b = A[idx], B[idx]
    if cnt[idx] == 1:
        v = (a + b) // 2
        heappush(bigpq, (-v, 3 * idx + 2))
        heappush(smallpq, (v, 3 * idx + 2))
    elif cnt[idx] == 2:
        if a > b:
            heappush(bigpq, (-a, 3 * idx))
            heappush(smallpq, (a, 3 * idx))
        else:
            heappush(bigpq, (-b, 3 * idx + 1))
            heappush(smallpq, (b, 3 * idx + 1))
    else:
        break
print(ans)