During the research on properties of the greatest common divisor (GCD) of a set of numbers, Ildar, a famous mathematician, introduced a brand new concept of the weakened common divisor (WCD) of a list of pairs of integers.

For a given list of pairs of integers (a_1, b_1), (a_2, b_2), ..., (a_n, b_n) their WCD is arbitrary integer greater than 1, such that it divides at least one element in each pair. WCD may not exist for some lists.

For example, if the list looks like [(12, 15), (25, 18), (10, 24)], then their WCD can be equal to 2, 3, 5 or 6 (each of these numbers is strictly greater than 1 and divides at least one number in each pair).

You're currently pursuing your PhD degree under Ildar's mentorship, and that's why this problem was delegated to you. Your task is to calculate WCD efficiently.

Input

The first line contains a single integer n (1 ≤ n ≤ 150 000) — the number of pairs.

Each of the next n lines contains two integer values a_i, b_i (2 ≤ a_i, b_i ≤ 2 ⋅ 10^9).

Output

Print a single integer — the WCD of the set of pairs. 

If there are multiple possible answers, output any; if there is no answer, print -1.

Examples

Input

3
17 18
15 24
12 15


Output

6

Input

2
10 16
7 17


Output

-1


Input

5
90 108
45 105
75 40
165 175
33 30


Output

5

Note

In the first example the answer is 6 since it divides 18 from the first pair, 24 from the second and 12 from the third ones. Note that other valid answers will also be accepted.

In the second example there are no integers greater than 1 satisfying the conditions.

In the third example one of the possible answers is 5. Note that, for example, 15 is also allowed, but it's not necessary to maximize the output.


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int[] arr = new int[100000];
        int n0 = Reader.nextInt();
        int m = n0;
        while (n0-->0){
            PriorityQueue<Integer> p = new PriorityQueue<>();
            int n1 = Reader.nextInt();
            int n2 = Reader.nextInt();
            while (n1%2==0)
            {
                //System.out.println(2 + " ");
                p.add(2);
                n1 /= 2;
            }

            // n must be odd at this point.  So we can
            // skip one element (Note i = i +2)
            for (int i = 3; i <= Math.sqrt(n1); i+= 2)
            {
                // While i divides n, print i and divide n
                while (n1%i == 0)
                {
                    //System.out.println(i + " ");
                    p.add(i);
                    n1 /= i;
                }
            }

            // This condition is to handle the case whien
            // n is a prime number greater than 2
            if (n1 > 2) {
                p.add(n1);
                //System.out.println(n1);
            }

            while (n2%2==0)
            {
                //System.out.println(2 + " ");
                p.add(2);
                n2 /= 2;
            }

            // n must be odd at this point.  So we can
            // skip one element (Note i = i +2)
            for (int i = 3; i <= Math.sqrt(n2); i+= 2)
            {
                // While i divides n, print i and divide n
                while (n2%i == 0)
                {
                    //System.out.println(i + " ");
                    p.add(i);
                    n2 /= i;
                }
            }

            // This condition is to handle the case when
            // n is a prime number greater than 2
            if (n2 > 2) {
                p.add(n2);
                //System.out.println(n2);
            }
            int prev = -1;
            int size = p.size();
            for (int i = 0 ; i < size; i ++){
                int x = p.poll();
                //System.out.println(x);
                if (x!=prev){
                    arr[x]++;
                }
                prev = x;
            }
            //System.out.println();
        }
        for (int i = 0 ; i < arr.length ; i++){
            if (arr[i]==m){
                System.out.println(i);
                break;

            }
        }
        System.out.println(-1);





    }

}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }

    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
