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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.Stack;
import java.util.TreeSet;
	
	
	
	                                            public class Solution1 implements Runnable
	                                            {
	                                                static final long MAX = 464897L;
	                                                static class InputReader
	                                                {
	                                                    private InputStream stream;
	                                                    private byte[] buf = new byte[1024];
	                                                    private int curChar;
	                                                    private int numChars;
	                                                    private SpaceCharFilter filter;
	                                                    private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	                                             
	                                                    public InputReader(InputStream stream)
	                                                    {
	                                                        this.stream = stream;
	                                                    }
	                                                    
	                                                    public int read()
	                                                    {
	                                                        if (numChars==-1) 
	                                                            throw new InputMismatchException();
	                                                        
	                                                        if (curChar >= numChars)
	                                                        {
	                                                            curChar = 0;
	                                                            try 
	                                                            {
	                                                                numChars = stream.read(buf);
	                                                            }
	                                                            catch (IOException e)
	                                                            {
	                                                                throw new InputMismatchException();
	                                                            }
	                                                            
	                                                            if(numChars <= 0)                
	                                                                return -1;
	                                                        }
	                                                        return buf[curChar++];
	                                                    }
	                                                 
	                                                    public String nextLine()
	                                                    {
	                                                        String str = "";
	                                                        try
	                                                        {
	                                                            str = br.readLine();
	                                                        }
	                                                        catch (IOException e)
	                                                        {
	                                                            e.printStackTrace();
	                                                        }
	                                                        return str;
	                                                    }
	                                                    public int nextInt()
	                                                    {
	                                                        int c = read();
	                                                        
	                                                        while(isSpaceChar(c)) 
	                                                            c = read();
	                                                        
	                                                        int sgn = 1;
	                                                        
	                                                        if (c == '-') 
	                                                        {
	                                                            sgn = -1;
	                                                            c = read();
	                                                        }
	                                                        
	                                                        int res = 0;
	                                                        do 
	                                                        {
	                                                            if(c<'0'||c>'9') 
	                                                                throw new InputMismatchException();
	                                                            res *= 10;
	                                                            res += c - '0';
	                                                            c = read();
	                                                        }
	                                                        while (!isSpaceChar(c)); 
	                                                        
	                                                        return res * sgn;
	                                                    }
	                                                    
	                                                    public long nextLong() 
	                                                    {
	                                                        int c = read();
	                                                        while (isSpaceChar(c))
	                                                            c = read();
	                                                        int sgn = 1;
	                                                        if (c == '-') 
	                                                        {
	                                                            sgn = -1;
	                                                            c = read();
	                                                        }
	                                                        long res = 0;
	                                                        
	                                                        do 
	                                                        {
	                                                            if (c < '0' || c > '9')
	                                                                throw new InputMismatchException();
	                                                            res *= 10;
	                                                            res += c - '0';
	                                                            c = read();
	                                                        }
	                                                        while (!isSpaceChar(c));
	                                                            return res * sgn;
	                                                    }
	                                                    
	                                                    public double nextDouble() 
	                                                    {
	                                                        int c = read();
	                                                        while (isSpaceChar(c))
	                                                            c = read();
	                                                        int sgn = 1;
	                                                        if (c == '-') 
	                                                        {
	                                                            sgn = -1;
	                                                            c = read();
	                                                        }
	                                                        double res = 0;
	                                                        while (!isSpaceChar(c) && c != '.') 
	                                                        {
	                                                            if (c == 'e' || c == 'E')
	                                                                return res * Math.pow(10, nextInt());
	                                                            if (c < '0' || c > '9')
	                                                                throw new InputMismatchException();
	                                                            res *= 10;
	                                                            res += c - '0';
	                                                            c = read();
	                                                        }
	                                                        if (c == '.') 
	                                                        {
	                                                            c = read();
	                                                            double m = 1;
	                                                            while (!isSpaceChar(c)) 
	                                                            {
	                                                                if (c == 'e' || c == 'E')
	                                                                    return res * Math.pow(10, nextInt());
	                                                                if (c < '0' || c > '9')
	                                                                    throw new InputMismatchException();
	                                                                m /= 10;
	                                                                res += (c - '0') * m;
	                                                                c = read();
	                                                            }
	                                                        }
	                                                        return res * sgn;
	                                                    }
	                                                    
	                                                    public String readString() 
	                                                    {
	                                                        int c = read();
	                                                        while (isSpaceChar(c))
	                                                            c = read();
	                                                        StringBuilder res = new StringBuilder();
	                                                        do 
	                                                        {
	                                                            res.appendCodePoint(c);
	                                                            c = read();
	                                                        } 
	                                                        while (!isSpaceChar(c));
	                                                        
	                                                        return res.toString();
	                                                    }
	                                                 
	                                                    public boolean isSpaceChar(int c) 
	                                                    {
	                                                        if (filter != null)
	                                                            return filter.isSpaceChar(c);
	                                                        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	                                                    }
	                                                 
	                                                    public String next() 
	                                                    {
	                                                        return readString();
	                                                    }
	                                                    
	                                                    public interface SpaceCharFilter 
	                                                    {
	                                                        public boolean isSpaceChar(int ch);
	                                                    }
	                                                }
	                                                 
	                                                public static void main(String args[]) throws Exception
	                                                {
	                                                    new Thread(null, new Solution1(),"Solution",1<<26).start();
	                                                }    
	                                                public static int gcd(int a, int b)
	                                                {
	                                                    if (a == 0)
	                                                        return b;
	                                                     
	                                                    return gcd(b%a, a);
	                                                }
	                                                int lcm(int a, int b)
	                                                {
	                                                    return (a*b)/gcd(a, b);
	                                                }
	                                                ArrayList<Integer> adj[];
	                                                ArrayList<Integer> adj1[];
	                                                static long MOD = 1000000007;
	                                                int[] dx = {1,-1,0,0};
	                                                int[] dy = {0,0,1,-1};
	                                                int MAXN = 100005;
	                                                long[] val;
	                                                public void run() 
	                                                {
	                                                    
	                                                        //InputReader sc= new InputReader(new FileInputStream("input.txt"));
	                                                        //PrintWriter w= new PrintWriter(new FileWriter("output.txt"));
	                                                        InputReader sc = new InputReader(System.in);
	                                                        PrintWriter w = new PrintWriter(System.out);
	                                                        
	                                                        int n = sc.nextInt();
	                                                        sieve();
	                                                        Pair[] p = new Pair[n];
	                                                        for(int i = 0;i < n;i++) {
	                                                        	p[i] = new Pair(sc.nextInt(),sc.nextInt());
	                                                        }
	                                                        if(n == 1) {
	                                                        	w.println(p[0].a);
	                                                        }else {
	                                                        	int[] calc = {p[0].a,p[0].b,p[1].a,p[1].b};
	                                                        	TreeSet<Integer> prs = new TreeSet();
	                                                        	for(int i = 0;i < 2;i++) {
	                                                        		for(int j : pr) {
	                                                        			while(calc[i] % j == 0) {
	                                                        				calc[i] = calc[i]/j;
	                                                        				prs.add(j);
	                                                        			}
	                                                        		}
	                                                        		prs.add(calc[i]);
	                                                        	}
	                                                        	TreeSet<Integer> ans = new TreeSet();
	                                                        	for(int i = 2;i < 4;i++) {
	                                                        		for(int j : pr) {
	                                                        			boolean flag = false;
	                                                        			while(calc[i] % j == 0) {
	                                                        				calc[i] = calc[i]/j;
	                                                        				flag = true;
	                                                        			}
	                                                        			if(flag && prs.contains(j)) {
	                                                        				ans.add(j);
	                                                        			}
	                                                        		}
	                                                        		if(prs.contains(calc[i])) {
	                                                        			ans.add(calc[i]);
	                                                        		}
	                                                        		
	                                                        	}
	                                                        	for(int i = 2;i < p.length;i++) {
	                                                        		ArrayList<Integer> toRemove = new ArrayList();
	                                                        		for(Integer x: ans) {
	                                                        			if(p[i].a % x != 0 && p[i].b % x != 0) {
	                                                        				toRemove.add(x);
	                                                        			}
	                                                        		}
	                                                        		for(Integer val: toRemove) {
	                                                        			ans.remove(val);
	                                                        		}
	                                                        	}
	                                                        	if(ans.size() == 0 || ans.last() == 1) {
	                                                        		w.println("-1");
	                                                        	}else {
	                                                        		w.println(ans.last());
	                                                        	}
	                                                        }
	                                                        w.close();	                                                                                                                      
	                                                 }
	                                                
	                                                boolean[] visited;
	                                                ArrayList<ArrayList<Integer>> ar = new ArrayList();
	                                                ArrayList<Integer> temp;
	                                                void dfs1(int a) {
	                                                	visited[a] = true;
	                                                	Iterator<Integer> it = adj1[a].iterator();
	                                                	while(it.hasNext()) {
	                                                		int x = it.next();
	                                                		if(!visited[x]) {
	                                                			dfs1(x);
	                                                		}
	                                                	}
	                                                	temp.add(a);
	                                                }
	                                                void topo() {
	                                                	for(int i = 0;i < adj.length;i++) {
	                                                		if(!visited[i]) {
	                                                			dfs(i);
	                                                		}
	                                                	}
	                                                }
	                                                Stack<Integer> st=  new Stack();
	                                                void dfs(int a) {
	                                                	visited[a] = true;
	                                                	Iterator<Integer> it = adj[a].iterator();
	                                                	while(it.hasNext()) {
	                                                		int x = it.next();
	                                                		if(!visited[x]) {
	                                                			dfs(x);
	                                                		}
	                                                	}
	                                                	st.add(a);
	                                                }
	                                               
	                                                ArrayList<Integer> pr = new ArrayList();
	                                                void sieve() {
	                    								boolean[] prime = new boolean[MAXN];
	                    								Arrays.fill(prime, true);
	                    								prime[1] = false;
	                    								for(int i = 2;i < MAXN;i++) {
	                    									if(prime[i]) {
	                    										for(int j = 2*i;j < MAXN;j+=i) {
	                    											prime[j] = false;
	                    										}
	                    									}
	                    								}
	                    								for(int i =2;i < MAXN;i++) {
	                    									if(prime[i]) {
	                    										pr.add(i);
	                    									}
	                    								}
	                    							}
	                                                TreeSet<Integer> factorize(int a) {
	                                                	TreeSet<Integer> ar = new TreeSet();
	                                                	while(a != 1) {
	                                                		ar.add(spf[a]);
	                                                		a = a/spf[a];
	                                                	}
	                                                	return ar;
	                                                }
	                    							int[] spf;
	                                                static class Pair implements Comparable<Pair>{
	                                                    int a;
	                                                    int b;
	                                                    
	                                                    
	                                                    Pair(int a,int b){
	                                                        this.a  =a;
	                                                        this.b = b;
	                                                        
	                                                    }
	                                                    Pair(){}    
	                                                    public boolean equals(Object o)
	                                                    {
	                                                        Pair p = (Pair)o;
	                                                        return (this.a == p.a && this.b == p.b) || (this.a == p.b && this.b == p.a);
	                                                    }
	                                                    
	                                                    public int compareTo(Pair p){
	                                                    	 return Integer.compare(this.b, p.b);
	                                                    }
	                                                    public int hashCode()
	                                                    {
	                                                        return new Long(a).hashCode()*31 + new Long(b).hashCode()*2 + new Long(a).hashCode() * 3;
	                                                    }
	
	                                                }
	                                                
	                                }