Problem:
Score : 700 points

Problem Statement

Aoki is playing with a sequence of numbers a_{1}, a_{2}, ..., a_{N}. Every second, he performs the following operation :

Choose a positive integer k. For each element of the sequence v, Aoki may choose to replace v with its remainder when divided by k, or do nothing with v. The cost of this operation is 2^{k} (regardless of how many elements he changes).

Aoki wants to turn the sequence into b_{1}, b_{2}, ..., b_{N} (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required.

Constraints

1 \leq N \leq 50

0 \leq a_{i}, b_{i} \leq 50

All values in the input are integers.

Input

Input is given from Standard Input in the following format:

N
a_{1} a_{2} ... a_{N}
b_{1} b_{2} ... b_{N}

Output

Print the minimum cost required to turn the original sequence into b_{1}, b_{2}, ..., b_{N}. If the task is impossible, output -1 instead.

Sample Input 1

3
19 10 14
0 3 4

Sample Output 1

160

Here's a possible sequence of operations :

Choose k = 7. Replace 19 with 5, 10 with 3 and do nothing to 14. The sequence is now 5, 3, 14.

Choose k = 5. Replace 5 with 0, do nothing to 3 and replace 14 with 4. The sequence is now 0, 3, 4.

The total cost is 2^{7} + 2^{5} = 160.

Sample Input 2

3
19 15 14
0 0 0

Sample Output 2

2

Aoki can just choose k = 1 and turn everything into 0. The cost is 2^{1} = 2.

Sample Input 3

2
8 13
5 13

Sample Output 3

-1

The task is impossible because we can never turn 8 into 5 using the given operation.

Sample Input 4

4
2 0 1 8
2 0 1 8

Sample Output 4

0

Aoki doesn't need to do anything here. The cost is 0.

Sample Input 5

1
50
13

Sample Output 5

137438953472

Beware of overflow issues.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using CompLib.Util;

public class Program
{
    private int N;
    private int[] A, B;
    private const int Inf = int.MaxValue;

    public void Solve()
    {
        var sc = new Scanner();


        // i->jの操作で使う最小の操作
        var l = new int[51, 51];
        for (int i = 0; i <= 50; i++)
        {
            for (int j = 0; j <= 50; j++)
            {
                l[i, j] = Inf;
            }
        }

        for (int i = 0; i <= 50; i++)
        {
            l[i, i] = 0;
            for (int d = 1; d <= i; d++)
            {
                l[i, i % d] = Math.Min(l[i, i % d], d);
            }

            for (int m = i - 1; m >= 0; m--)
            {
                if (l[i, m] == Inf) continue;
                for (int j = m - 1; j >= 0; j--)
                {
                    if (l[m, j] == Inf) continue;
                    l[i, j] = Math.Min(l[i, j], Math.Max(l[i, m], l[m, j]));
                }
            }
        }

        N = sc.NextInt();
        A = sc.IntArray();
        B = sc.IntArray();
        bool f = false;
        long ans = 0;
        for (int i = 0; i < N; i++)
        {
            if (A[i] != B[i])
            {
                f = true;
                break;
            }
        }

        while (f)
        {
            bool nextF = false;
            int max = 0;
            bool ff = false;
            for (int i = 0; i < N; i++)
            {
                if (l[A[i], B[i]] == Inf) continue;
                if (A[i] == B[i]) continue;
                ff = true;
                max = Math.Max(max, l[A[i], B[i]]);
            }

            if (!ff)
            {
                Console.WriteLine("-1");
                return;
            }

            for (int i = 0; i < N; i++)
            {
                if (A[i] == B[i]) continue;
                if (A[i] % max >= B[i] && l[A[i], B[i]] >= l[A[i] % max, B[i]])
                {
                    A[i] %= max;
                }

                if (A[i] != B[i]) nextF = true;
            }

            ans |= 1L << max;
            f = nextF;
            // Console.WriteLine(string.Join(" ",A));
        }

        Console.WriteLine(ans);
    }

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}