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.util.*;

public class r505_b extends Template{
	public static long g(long a, long b){
		if ( a % b == 0 ) return b;
		else if (b % a == 0) return a;
		else if ( a > b ) return g(a%b, b);
		else return g(b%a, a);
	}

	public static long pf(long gcd){
		for(int i=2; i<(int)Math.sqrt(gcd)+1; i++){
			if(gcd%i==0) return i;
		}
		return gcd;
	}

	public static void main(String[] args) {
		int n = nI();
		long a, b, c, d;
		a = nL(); b = nL();
		long prod = a*b;
		long gcd = prod/g(a, b);
		int flag = 0;
		for(int i = 1; i < n; i++){
			c = nL(); d = nL();
			gcd = g(gcd, c*d)/g(c, d);
		}
		if(gcd == 1){ pn(-1); return;}
		long ans = g(gcd, a);
		if(ans==1) ans = g(gcd, b);
		if(ans==1) ans = pf(gcd); 
		pn(ans);
	}
}

class Template{
	static Scanner s = new Scanner(System.in);
	final static int nI(){return s.nextInt();}
	final static long nL(){return s.nextLong();}
	final static String nS(){return s.nextLine();}
	/* Renaming of some generic utility classes */
	final static class mylist extends ArrayList<pair>{}
	/* Constants Section */
	final static int INT_MIN = Integer.MIN_VALUE ;
	final static int INT_MAX = Integer.MAX_VALUE ;
	final static long LONG_MIN = Long.MIN_VALUE ;
	final static long LONG_MAX = Long.MAX_VALUE ;
	static long MOD = 1000000007 ;
	static void p(){System.out.println();}
	static void pn(long a){System.out.println(a);}
	static void pn(mylist a){System.out.println(a);}
	static void p(long a){System.out.printf("%d ", a);}
	static void p(long a, long b){System.out.printf("%d %d\n", a, b);}
	static void p(long a, long b, long c){System.out.printf("%d %d %d\n", a, b, c);}
	/* Implementation of operations modulo MOD */
	static long inv(long a){ return powM(a,MOD-2) ; }
	static long m(long a,long b){ return (a*b)%MOD ; }
	static long d(long a,long b){ return (a*inv(b))%MOD ; }
	static long powM(long a,long b){
		if(b<0) return powM(inv(a),-b) ;
		long ans=1 ;
		for( ; b!=0 ; a=(a*a)%MOD , b/=2) if((b&1)==1) ans = (ans*a)%MOD ;
		return ans ;
	}
}
class pair implements Comparable<pair>{
	long x ; long y ;
	pair(long _x,long _y){ x=_x ; y=_y ;}
	public int compareTo(pair p){
		return (this.x<p.x ? -1 : (this.x>p.x ? 1 : (this.y<p.y ? -1 : (this.y>p.y ? 1 : 0)))) ;
	}
	public String toString(){ return "(" + x + " " + y+ ")";}
}