import sys
input = sys.stdin.readline
from bisect import bisect_left
mod = 998244353


class SparseTable():
    def __init__(self, A, STfunc):
        # A: 処理したい数列
        self.N = len(A)
        self.K = self.N.bit_length() - 1
        self.table = [0] * (self.N * (self.K + 1))
        self.STfunc = STfunc
        for i, a in enumerate(A):
            self.table[i] = a
        for k in range(1, self.K + 1):
            for i in range(self.N):
                j = i + (1 << (k-1))
                if j <= self.N-1:
                    self.table[i + k * self.N] = STfunc(self.table[i + (k-1) * self.N], self.table[j + (k-1) * self.N])

    def query(self, l, r):
        l -= 1
        r -= 1
        # [l, r)の最小値を求める
        k = (r-l).bit_length() - 1
        return self.STfunc(self.table[l + k * self.N], self.table[r - (1 << k) + k * self.N])


class SegmentTree:
    def __init__(self, A, initialize=True, segfunc=min, ident=2000000000):
        self.N = len(A)
        self.LV = (self.N - 1).bit_length()
        self.N0 = 1 << self.LV
        self.segfunc = segfunc
        self.ident = ident
        if initialize:
            self.data = [self.ident] * self.N0 + A + [self.ident] * (self.N0 - self.N)
            for i in range(self.N0 - 1, 0, -1):
                self.data[i] = segfunc(self.data[i * 2], self.data[i * 2 + 1])
        else:
            self.data = [self.ident] * (self.N0 * 2)

    def update(self, i, x):
        i += self.N0 - 1
        self.data[i] = x
        for _ in range(self.LV):
            i >>= 1
            self.data[i] = self.segfunc(self.data[i * 2], self.data[i * 2 + 1])

    def get(self, i):
        return self.data[i + self.N0 - 1]

    # open interval [l, r)
    def query(self, l, r):
        l += self.N0 - 1
        r += self.N0 - 1
        ret_l = self.ident
        ret_r = self.ident
        while l < r:
            if l & 1:
                ret_l = self.segfunc(ret_l, self.data[l])
                l += 1
            if r & 1:
                ret_r = self.segfunc(self.data[r - 1], ret_r)
                r -= 1
            l >>= 1
            r >>= 1
        return self.segfunc(ret_l, ret_r)

    # return smallest i(l <= i < r) s.t. check(A[i]) == True
    def binsearch(self, l, r, check):
        if not check(self.query(l, r)):
            return r
        l += self.N0 - 1
        val = self.ident
        while True:
            if check(self.segfunc(val, self.data[l])):
                break
            if l & 1:
                val = self.segfunc(val, self.data[l])
                l += 1
            l >>= 1
        while l < self.N0:
            newval = self.segfunc(val, self.data[l * 2])
            if not check(newval):
                val = newval
                l = (l << 1) + 1
            else:
                l <<= 1
        return l - self.N0 + 1


N = int(input())
A_ori = list(map(int, input().split()))
B_ori = list(map(int, input().split()))

X = []
for a, b in zip(A_ori, B_ori):
    if a > b:
        a, b = b, a
    X.append((a, b, (a + b) // 2))
X.sort(key=lambda x: x[2])

A = []
B = []
AB = []
val = set()
for a, b, ab in X:
    A.append(a)
    B.append(b)
    AB.append(ab)
    val.add(a)
    val.add(b)
    val.add(ab)

ST_A_min = SparseTable(A, min)
ST_A_max = SparseTable(A, max)
ST_B_min = SegmentTree(B)
ST_B_max = SegmentTree(B, initialize=True, segfunc=max, ident=-2000000000)

ans = min(max(A) - min(A), max(B) - min(B))
for v in sorted(list(val)):
    i = bisect_left(AB, v)

    if i != 0:
        mi_B = ST_B_min.query(1, i + 1)
        ma_B = ST_B_max.query(1, i + 1)
        if mi_B < v:
            continue
    else:
        ma_B = -1
        mi_B = 10 ** 10

    ok = max(ma_B, AB[-1])
    if i == 0:
        ng = v - 1
    else:
        ng = min(v, ma_B) - 1
    if (ng + 1) - v >= ans:
        continue
    mid = (ok + ng) // 2
    while ok - ng > 1:
        r = bisect_left(AB, mid + 1)
        flg = 1
        if r != N:
            mi_A = ST_A_min.query(r+1, N+1)
            ma_A = ST_A_max.query(r+1, N+1)
            if mi_A < v or ma_A > mid:
                flg = 0
        if flg:
            ok = mid
        else:
            ng = mid
        mid = (ok + ng) // 2
    ans = min(ans, ok - v)

print(ans)