import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }




void main() {
  try {
    for (; ; ) {
      const N = readInt;
      auto A = new long[N]; foreach (i; 0 .. N) A[i] = readLong;
      auto B = new long[N]; foreach (i; 0 .. N) B[i] = readLong;
      foreach (i; 0 .. N) {
        if (A[i] > B[i]) {
          swap(A[i], B[i]);
        }
      }
      
      alias Entry = Tuple!(long, "val", int, "i", int, "s");
      BinaryHeap!(Array!Entry, "a.val > b.val") que;
      long mx = long.min;
      foreach (i; 0 .. N) {
        que.insert(Entry(A[i], i, 0));
        chmax(mx, A[i]);
      }
      
      long ans = long.max;
      for (; ; ) {
        debug {
          writeln(que.front, " ", mx);
        }
        const mn = que.front.val;
        const i = que.front.i;
        const s = que.front.s;
        que.removeFront;
        chmin(ans, mx - mn);
        if (s == 0) {
          que.insert(Entry((A[i] + B[i]) / 2, i, 1));
          chmax(mx, (A[i] + B[i]) / 2);
        } else if (s == 1) {
          que.insert(Entry(B[i], i, 2));
          chmax(mx, B[i]);
        } else {
          break;
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}