import java.io.*;
import java.util.*;
import java.util.stream.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner();
        int n = sc.nextInt();
        int[] valuesA = new int[n];
        for (int i = 0; i < n; i++) {
            valuesA[i] = sc.nextInt();
        }
        TreeSet<Integer> mins = new TreeSet<>();
        TreeSet<Unit> units = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            int x = sc.nextInt();
            mins.add(x);
            mins.add(valuesA[i]);
            mins.add((x + valuesA[i]) / 2);
            units.add(new Unit(i, x, valuesA[i]));
        }
        int ans = Integer.MAX_VALUE;
        boolean cont = true;
        for (int x : mins) {
            while (units.first().getValue() < x) {
                Unit y = units.pollFirst();
                if (!y.add()) {
                    cont = false;
                    break;
                }
                units.add(y);
            }
            if (!cont) {
                break;
            }
            ans = Math.min(ans, units.last().getValue() - x);
        }
        System.out.println(ans);
    }
    
    static class Unit implements Comparable<Unit> {
        int current;
        int idx;
        int[] values;
        
        public Unit(int idx, int a, int b) {
            this.idx = idx;
            values = new int[]{a, b, (a + b) / 2};
            Arrays.sort(values);
        }
        
        public int hashCode() {
            return idx;
        }
        
        public boolean equals(Object o) {
            Unit x = (Unit)o;
            return idx == x.idx;
        }
        
        public int compareTo(Unit another) {
            if (getValue() == another.getValue()) {
                return idx - another.idx;
            } else {
                return getValue() - another.getValue();
            }
        }
        
        public int getValue() {
            return values[current];
        }
        
        public boolean add() {
            if (current == 2) {
                return false;
            } else {
                current++;
                return true;
            }
        }
    }
}
class Utilities {
    static String arrayToLineString(Object[] arr) {
        return Arrays.stream(arr).map(x -> x.toString()).collect(Collectors.joining("\n"));
    }
    
    static String arrayToLineString(int[] arr) {
        return String.join("\n", Arrays.stream(arr).mapToObj(String::valueOf).toArray(String[]::new));
    }
}
class Scanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    StringBuilder sb = new StringBuilder();
    
    public Scanner() throws Exception {
        
    }
    
    public int nextInt() throws Exception {
        return Integer.parseInt(next());
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(next());
    }
    
    public double nextDouble() throws Exception {
        return Double.parseDouble(next());
    }
    
    public int[] nextIntArray() throws Exception {
        return Stream.of(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
    }
    
    public String next() throws Exception {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }
    
}