Problem: 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.

Solution (in JAVA):

Solution:
import java.util.*;


import java.io.*;
import java.math.*;
public class A
	
	{ 
		 static FastReader sc=new FastReader(); 
		 
			  public static void main(String[] args)
	    {
				    //CHECK FOR N=1
	       	//CHECK FOR N=1
		    //CHECK FOR N=1
	       	//CHECK FOR N=1
		  
		  PrintWriter out=new PrintWriter(System.out);
		  StringBuffer sb=new StringBuffer("");
	  int ttt=1;
	    // ttt =i(); 
	 
        outer :while (ttt-- > 0) 
		{
        	int n=i();
        	int A[]=new int[n];
        	int B[]=new int[n];
        	input(A, B);
        	HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
        	for(int i=2;i*i<=A[0];i++) {
        		if(A[0]%i==0) {
        			while(A[0]%i==0) {
        				A[0]/=i;
        				map.put(i, 1);
        			}
        		}
        	}
        	if(A[0]>1) {
        		map.put(A[0],1);
        	}
        	A[0]=B[0];
        	for(int i=2;i*i<=A[0];i++) {
        		if(A[0]%i==0) {
        			while(A[0]%i==0) {
        				A[0]/=i;
        				map.put(i, 1);
        			}
        		}
        	}
        	if(A[0]>1) {
        		map.put(A[0],1);
        	}
        	for(int i : map.keySet()) {
        		int f=-1;
        		for(int j=1;j<n;j++) {
        			if(A[j]%i!=0 && B[j]%i!=0) {
        				f=1;
        				break;
        			}
        		}
        		if(f==-1) {
        			System.out.println(i);
        			return;
        		}
        	}
        	System.out.println("-1");
        	
        	
        	
		}
	   out.close();
      // System.out.println(sb.toString());
       
       
       //CHECK FOR N=1                    //CHECK FOR M=0
        //CHECK FOR N=1                    //CHECK FOR M=0
       	//CHECK FOR N=1
       	//CHECK FOR N=1
       	//CHECK FOR N=1
    }
			  
				  
				  
  




static int[] input(int n) {
  	int A[]=new int[n];
  	   for(int i=0;i<n;i++) {
  		   A[i]=sc.nextInt();
  	   }
  	   return A;
     }
  static long[] inputL(int n) {
  	long A[]=new long[n];
  	   for(int i=0;i<n;i++) {
  		   A[i]=sc.nextLong();
  	   }
  	   return A;
     }
  static String[] inputS(int n) {
  	String A[]=new String[n];
  	   for(int i=0;i<n;i++) {
  		   A[i]=sc.next();
  	   }
  	   return A;
     }
  static long sum(int A[]) {
  	long sum=0;
  	for(int i : A) {
  		sum+=i;
  	}
  	return sum;
  }
  static long sum(long A[]) {
  	long sum=0;
  	for(long i : A) {
  		sum+=i;
  	}
  	return sum;
  }

  static void input(int A[],int B[]) {
  	   for(int i=0;i<A.length;i++) {
  		   A[i]=sc.nextInt();
  		   B[i]=sc.nextInt();
  	   }
  }
  static int[][] input(int n,int m){
  	int A[][]=new int[n][m];
  	for(int i=0;i<n;i++) {
  		for(int j=0;j<m;j++) {
  			A[i][j]=i();
  		}
  	}
  	return A;
  }
  static char[][] charinput(int n,int m){
  	char A[][]=new char[n][m];
  	for(int i=0;i<n;i++) {
  		String s=s();
  		for(int j=0;j<m;j++) {
  			A[i][j]=s.charAt(j);
  		}
  	}
  	return A;
  }
  static int max(int A[]) {
  	int max=Integer.MIN_VALUE;
  	for(int i=0;i<A.length;i++) {
  		max=Math.max(max, A[i]);
  	}
  	return max;
  }
  static int min(int A[]) {
  	int min=Integer.MAX_VALUE;
  	for(int i=0;i<A.length;i++) {
  		min=Math.min(min, A[i]);
  	}
  	return min;
  }
  static long max(long A[]) {
  	long max=Long.MIN_VALUE;
  	for(int i=0;i<A.length;i++) {
  		max=Math.max(max, A[i]);
  	}
  	return max;
  }
  static long min(long A[]) {
  	long min=Long.MAX_VALUE;
  	for(int i=0;i<A.length;i++) {
  		min=Math.min(min, A[i]);
  	}
  	return min;
  }
  static long mod(long x) {
  	 int mod=1000000007;
  	  return ((x%mod + mod)%mod);
  }
  static String reverse(String s) {
  	StringBuffer p=new StringBuffer(s);
  	p.reverse();
  	return p.toString();
  }

       static int i() {
      	 return sc.nextInt();
       }
       static String s() {
      	 return sc.next();
       }
       static long l() {
      	 return sc.nextLong();
       }  
       static void sort(int[] A){
          int n = A.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i){
              int tmp = A[i];
              int randomPos = i + rnd.nextInt(n-i);
              A[i] = A[randomPos];
              A[randomPos] = tmp;
          }
          Arrays.sort(A);
       }
       static void sort(long[] A){
  	        int n = A.length;
  	        Random rnd = new Random();
  	        for(int i=0; i<n; ++i){
  	            long tmp = A[i];
  	            int randomPos = i + rnd.nextInt(n-i);
  	            A[i] = A[randomPos];
  	            A[randomPos] = tmp;
  	        }
  	        Arrays.sort(A);
  	     }
    static String sort(String s) {
   	 Character ch[]=new Character[s.length()];
   	 for(int i=0;i<s.length();i++) {
   		 ch[i]=s.charAt(i);
   	 }
   	 Arrays.sort(ch);
   	 StringBuffer st=new StringBuffer("");
 for(int i=0;i<s.length();i++) {
	 st.append(ch[i]);
 }
 return st.toString();
}
static HashMap<Integer,Integer> hash(int A[]){
  HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
  for(int i : A) {
	  if(map.containsKey(i)) {
		  map.put(i, map.get(i)+1);
	  }
	  else {
		  map.put(i, 1);
	  }
  }
  return map;
}
static HashMap<Long,Integer> hash(long A[]){
	  HashMap<Long,Integer> map=new HashMap<Long, Integer>();
	  for(long i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
	}
static TreeMap<Integer,Integer> tree(int A[]){
  TreeMap<Integer,Integer> map=new TreeMap<Integer, Integer>();
  for(int i : A) {
	  if(map.containsKey(i)) {
		  map.put(i, map.get(i)+1);
	  }
	  else {
		  map.put(i, 1);
	  }
  }
  return map;
}
static TreeMap<Long,Integer> tree(long A[]){
	  TreeMap<Long,Integer> map=new TreeMap<Long, Integer>();
	  for(long i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
	}
   static boolean prime(int n) 
    { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        double sq=Math.sqrt(n);
  
        for (int i = 5; i <= sq; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 
   static boolean prime(long n) 
    { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        double sq=Math.sqrt(n);
  
        for (int i = 5; i <= sq; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 
   static int gcd(int a, int b) 
   { 
       if (a == 0) 
           return b; 
       return gcd(b % a, a); 
   } 
   static long gcd(long a, long b) 
   { 
       if (a == 0) 
           return b; 
       return gcd(b % a, a); 
   } 
   static class Pair implements Comparable<Pair>
   {
  	 int x;
  	 int y;
  	 Pair(int x,int y){
  		 this.x=x;
  		 this.y=y;
  	 }
	@Override
	public int compareTo(Pair o) {
		if(this.x>o.x)
			return 1;
		else if(this.x<o.x)
			return -1;
		else {
			if(this.y<o.y)
				return 1;
			else if(this.y>o.y)
				return -1;
			else
				return 0;
		}
	}
   }
      
  static class FastReader 
  { 
      BufferedReader br; 
      StringTokenizer st; 

      public FastReader() 
      { 
          br = new BufferedReader(new
                   InputStreamReader(System.in)); 
      } 

      String next() 
      { 
          while (st == null || !st.hasMoreElements()) 
          { 
              try
              { 
                  st = new StringTokenizer(br.readLine()); 
              } 
              catch (IOException  e) 
              { 
                  e.printStackTrace(); 
              } 
          } 
          return st.nextToken(); 
      } 

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

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

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

      String nextLine() 
      { 
          String str = ""; 
              try
              { 
                  str = br.readLine(); 
              } 
              catch (IOException e) 
              { 
                  e.printStackTrace(); 
              } 
              return str; 
          } 
      } 
  }