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.awt.List;
	import java.io.*;
	import java.lang.*;
import java.lang.reflect.Array;
		
	public class code4
		{
	 	public static void main(String[] args)
			{
				InputReader in = new InputReader(System.in);
				PrintWriter pw = new PrintWriter(System.out);
				
				//Code starts..
				

				int n = in.nextInt();
				int[][] a = new int[n][2];
				for(int i=0; i<n; i++)
				{
					a[i][0] = in.nextInt();
					a[i][1] = in.nextInt();
					
				}
				
				int a1 = a[n-1][0];
				int a2 = a[n-1][1];
				HashSet<Long>[] set = new HashSet[2]; 
				HashSet<Long> fset = new HashSet<>();
				
					
					set[0] = new HashSet<>();
					set[1] = new HashSet<>();
					set[0] = fact2(a[n-1][0], fset);
					set[1] = fact2(a[n-1][1], fset);
				
				long ans = -1;
				for(long p: set[0])
				{
					boolean flag = true;
					for(int i=0; i<n; i++)
					{	
						
						if(a[i][0]%p !=0 && a[i][1]%p!=0)
						{
							flag = false;
							break;
						}
						
					}
					
					if(flag)
					{
						ans = p;
						break;
				}
					
				}
				
				if(ans==-1)
				for(long p: set[1])
				{
					boolean flag = true;
					for(int i=0; i<n; i++)
					{	
						
						if(a[i][0]%p !=0 && a[i][1]%p!=0)
						{
							flag = false;
							break;
						}
						
					}
					
					if(flag)
					{
						ans = p;
						break;
				}
				}
				
				if(n==1)
					ans = a[0][0];
				
				pw.println(ans);
				
				//Code ends....
				
				pw.flush();
				pw.close();
			}
		
	 	public static HashSet<Long> fact2(long n, HashSet<Long> s2)
	 	{
	 		HashSet<Long> set = new HashSet<>();
	 		
	 		for(long i=2; i*i<=n; i++)
	 		{
	 			if(n%i==0)
	 			{
	 				set.add(i);
	 				set.add(n/i);

	 			}
	 		}
	 		set.add(n);
	 		
	 		
	 		return set;
	 		
	 	}
	 	
	 	
			static class InputReader 
			{
				 
				private final InputStream stream;
				private final byte[] buf = new byte[8192];
				private int curChar, snumChars;
				private SpaceCharFilter filter;
		 
				public InputReader(InputStream stream) 
				{
					this.stream = stream;
				}
		 
				public int snext() 
				{
					if (snumChars == -1)
						throw new InputMismatchException();
					if (curChar >= snumChars) 
					{
						curChar = 0;
						try 
						{
							snumChars = stream.read(buf);
						} 
						catch (IOException e) 
						{
							throw new InputMismatchException();
						}
						if (snumChars <= 0)
							return -1;
					}
					return buf[curChar++];
				}
		 
				public int nextInt() 
			    {
					int c = snext();
					while (isSpaceChar(c)) 
					{
						c = snext();
					}
					int sgn = 1;
					if (c == '-')
				    {
						sgn = -1;
						c = snext();
					}
					int res = 0;
					do 
					{
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = snext();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
		 
				public long nextLong()
			    {
					int c = snext();
					while (isSpaceChar(c)) 
					{
						c = snext();
					}
					int sgn = 1;
					if (c == '-') 
					{
						sgn = -1;
						c = snext();
					}
					long res = 0;
					do 
					{
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = snext();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
		 
				public int[] nextIntArray(int n) 
				{
					int a[] = new int[n];
					for (int i = 0; i < n; i++) 
					{
						a[i] = nextInt();
					}
					return a;
				}
		 
				public String readString()
			    {
					int c = snext();
					while (isSpaceChar(c)) 
					{
						c = snext();
					}
					StringBuilder res = new StringBuilder();
					do 
					{
						res.appendCodePoint(c);
						c = snext();
					} while (!isSpaceChar(c));
					return res.toString();
				}
		 
				public String nextLine() 
				{
					int c = snext();
					while (isSpaceChar(c))
						c = snext();
					StringBuilder res = new StringBuilder();
					do 
					{
						res.appendCodePoint(c);
						c = snext();
					} while (!isEndOfLine(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;
				}
		 
				private boolean isEndOfLine(int c) 
				{
					return c == '\n' || c == '\r' || c == -1;
				}
		 
				public interface SpaceCharFilter
			    {
					public boolean isSpaceChar(int ch);
				}
			}
			public static long c = 0;
			
			public static long mod = 1000000007;
			public static int d;
			public static int p;
			public static int q;
			public static boolean flag;
			public static long INF= Long.MAX_VALUE;
			
			
			public static double slope(pair p1, pair p2)
			{
				double m = INF;
				if((p1.x - p2.x)!=0)
				m =  p1.y - p2.y/(p1.x - p2.x); 
				
				
				return Math.abs(m);
				
			}
			
			public static int gcd(long i, long l) {
				if (i == 0)
					return (int) l;
				return gcd(l % i, i);
			}
	
			
			
			/*public static int findGCD(int arr[], int n)
			{
			    int result = arr[0];
			    for (int i=1; i<n; i++)
			        result = gcd(arr[i], result);
			 
			    return result;
			}
			*/
			
		
	 
		
			
			
			
			
		    public static long lcm(int[] numbers) {
		        long lcm = 1;
		        int divisor = 2;
		        while (true) {
		            int cnt = 0;
		            boolean divisible = false;
		            for (int i = 0; i < numbers.length; i++) {
		                if (numbers[i] == 0) {
		                    return 0;
		                } else if (numbers[i] < 0) {
		                    numbers[i] = numbers[i] * (-1);
		                }
		                if (numbers[i] == 1) {
		                    cnt++;
		                }
		                if (numbers[i] % divisor == 0) {
		                    divisible = true;
		                    numbers[i] = numbers[i] / divisor;
		                }
		            }
		            if (divisible) {
		                lcm = lcm * divisor;
		            } else {
		                divisor++;
		            }
		            if (cnt == numbers.length) {
		                return lcm;
		            }
		        }
		    }
			public static long fact(long n) {
				
				long factorial = 1;
				 for(int i = 1; i <= n; i++)
			        {
			            factorial *= i;
			        }
				 return factorial;
			}
			
			public static void factSieve(int[] a, int n) {
				
				
				for(int i=2; i<=n; i+=2)
					a[i] = 2;
				
				
				for(int i=3; i<=n; i+=2)
				{
					if(a[i]==0)
					{
						a[i] = i;
						
						for(int j=i; j*i<=n; j++)
						{
							a[i*j] = i;	
						}
					}
				}
				
				int k = 1000;
				while(k!=1)
				{
					System.out.print(a[k]+" ");
					k /= a[k];
					
				}
			}
		
			
			
			public static long choose(long total, long choose){
			    if(total < choose)
			        return 0;
			    if(choose == 0 || choose == total)
			        return 1;
			    return (choose(total-1,choose-1)+choose(total-1,choose))%mod;
			}
			
			public static long[] suffle(long[] a,Random gen)
			{
				int n = a.length;
				for(int i=0;i<n;i++)
				{
					int ind = gen.nextInt(n-i)+i;
					long temp = a[ind];
					a[ind] = a[i];
					a[i] = temp;
				}
				return a;
			}
			
			public static long[] sort(long[] a)
			{
				Random gen = new Random();
				int n = a.length;
				for(int i=0;i<n;i++)
				{
					int ind = gen.nextInt(n-i)+i;
					long temp = a[ind];
					a[ind] = a[i];
					a[i] = temp;
				}
				
				Arrays.sort(a);
				return a;
			}
			
			public static int[] sort(int[] a)
			{
				Random gen = new Random();
				int n = a.length;
				for(int i=0;i<n;i++)
				{
					int ind = gen.nextInt(n-i)+i;
					int temp = a[ind];
					a[ind] = a[i];
					a[i] = temp;
				}
				
				Arrays.sort(a);
				return a;
			}
			
			public static int floorSearch(int arr[], int low, int high, int x)
			{
			    if (low > high)
			        return -1;
			 
			    if (x > arr[high])
			        return high;
			    int mid = (low+high)/2;
			 
			 
			    if (mid > 0 && arr[mid-1] < x && x < arr[mid])
			        return mid-1;
			 
			    if (x < arr[mid])
			        return floorSearch(arr, low, mid-1, x);
			 
			    return floorSearch(arr, mid+1, high, x);
			}
			
			
			public static void swap(int a, int b){
				int temp = a;
				a = b;
				b = temp;
			}
			public static ArrayList<Integer> primeFactorization(int n)
			{
				ArrayList<Integer> a =new ArrayList<Integer>();
				for(int i=2;i*i<=n;i++)
				{
					while(n%i==0)
					{
						a.add(i);
						n/=i;
					}
				}
				if(n!=1)
					a.add(n);
				return a;
			}
			
			
			public static void sieve(boolean[] isPrime,int n)
			{
				for(int i=1;i<n;i++)
					isPrime[i] = true;
				
				isPrime[0] = false;
				isPrime[1] = false;
				
				for(int i=2;i*i<n;i++)
				{
					if(isPrime[i] == true)
					{
						for(int j=(2*i);j<n;j+=i)
							isPrime[j] = false;
					}
				}
			}
			
			public static int lowerbound(ArrayList<Integer> list, int c2) {
				int i=Collections.binarySearch(list, c2);
				if(i<0)
					i = -(i+2);
				return i;
				
				
			}
			
			public static int lowerboundArray(long[] psum, long c2) {
				int i=Arrays.binarySearch(psum, c2);
				if(i<0)
					i = -(i+2);
				return i;
				
				
			}
			
			public static int uperboundArray(long[] psum, long c2) {
				int i=Arrays.binarySearch(psum, c2);
				if(i<0)
					i = -(i+1);
				return i;
				
				
			}
			
			
			public static int uperbound(ArrayList<Integer> list, int c2) {
				int i=Collections.binarySearch(list, c2);
				if(i<0)
					i = -(i+1);
				return i;
				
				
			}

			public static void print(int[] a)
			{
				PrintWriter pw = new PrintWriter(System.out);
				for(int i=0; i<a.length; i++)
					pw.print(a[i]+" ");
				
				pw.println();
				pw.flush();
				pw.close();
				
			}
			
			public static void print(long[] a)
			{
				PrintWriter pw = new PrintWriter(System.out);
				for(int i=0; i<a.length; i++)
					pw.print(a[i]+" ");
				
				pw.println();
				pw.flush();
				pw.close();
				
			}
			
			public static int GCD(int a,int b)
			{
				if(b==0)
					return a;
				else
					return GCD(b,a%b);
			}
			
			public static long GCD(long a,long b)
			{
				if(b==0)
					return a;
				else
					return GCD(b,a%b);
			}
			
			public static void extendedEuclid(int A,int B)
			{
				if(B==0)
				{
					d = A;
					p = 1 ;
					q = 0;
				}
				else
				{
					extendedEuclid(B, A%B);
					int temp = p;
					p = q;
					q = temp - (A/B)*q;
				}
			}
			
			public static long LCM(long a,long b)
			{
				return (a*b)/GCD(a,b);
			}
			
			public static int LCM(int a,int b)
			{
				return (a*b)/GCD(a,b);
			}
			
			public static int binaryExponentiation(int x,int n)
			{
			    int result=1;
			    while(n>0)
			    {
			        if(n % 2 ==1)
			            result=result * x;
			        x=x*x;
			        n=n/2;
			    }
			    return result;
			}
			
			
			public static int[] countDer(int n)
		    {
		        int der[] = new int[n + 1];
		     
		        der[0] = 1;
		        der[1] = 0;
		        der[2] = 1;
		     
		        for (int i = 3; i <= n; ++i)
		            der[i] = (i - 1) * (der[i - 1] + der[i - 2]);
		     
		        // Return result for n
		        return der;
		    }
			
			
			 static long binomialCoeff(int n, int k)
			    {
			    long C[][] = new long[n+1][k+1];
			    int i, j;
			     
			        // Calculate  value of Binomial Coefficient in bottom up manner
			    for (i = 0; i <= n; i++)
			    {
			        for (j = 0; j <= Math.min(i, k); j++)
			        {
			            // Base Cases
			            if (j == 0 || j == i)
			                C[i][j] = 1;
			      
			            // Calculate value using previosly stored values
			            else
			                C[i][j] = C[i-1][j-1] + C[i-1][j];
			          }
			     }
			      
			    return C[n][k];
			    }
			
			public static long binaryExponentiation(long x,long n)
			{
			    long result=1;
			    while(n>0)
			    {
			        if(n % 2 ==1)
			            result= (result * x)%mod;
			        x=(x%mod * x%mod)%mod;
			        n=n/2;
			    }
			    return result%mod;
			}
			
			public static int modularExponentiation(int x,int n,int M)
			{
			    int result=1;
			    while(n>0)
			    {
			        if(n % 2 ==1)
			            result=(result * x)%M;
			        x=(x%M*x%M)%M;
			        n=n/2;
			    }
			    return result;
			}
			
			public static long modularExponentiation(long x,long n,long M)
			{
			    long result=1;
			    while(n>0)
			    {
			        if(n % 2 ==1)
			            result=(result %M* x%M)%M;
			        x=(x*x)%M;
			        n=n/2;
			    }
			    return result;
			}
			
			public static int modInverse(int A,int M)
			{
			    return modularExponentiation(A,M-2,M);
			}
			
			public static long modInverse(long A,long M)
			{
			    return modularExponentiation(A,M-2,M);
			}
			
			
			public static boolean checkYear(int year)
		    {
				if (year % 400 == 0)
		            return true;
		     
		        if (year % 100 == 0)
		            return false;
		     
		        if (year % 4 == 0)
		            return true;
		        return false;
		    }
			
			public static boolean isPrime(int n)
			{
			    
			    if (n <= 1)  return false;
			    if (n <= 3)  return true;
			    
			    if (n%2 == 0 || n%3 == 0) 
			    	return false;
			 
			    for (int i=5; i*i<=n; i=i+6)
			    {
			        if (n%i == 0 || n%(i+2) == 0)
			           return false;
			    }
			    
			    return true;
			}
			
			static class pair implements Comparable<pair>
	 
			{
				Long x;
				Integer y;
				pair(long a,int y)
				{
					this.x=a;
					this.y=y;
				}
				
				public int compareTo(pair o) {
					int result = x.compareTo(o.x);
					if(result==0)
						result = y.compareTo(o.y);
					
					return result;
				}  
				
				public String toString()
				{
					return x+" "+y;
				}
				
				public boolean equals(Object o)
				{
					if (o instanceof pair)
				    {
						pair p = (pair)o;
						return p.x == x && p.y == y ;
					}
					return false;
				}
				
				public int hashCode()
				{
					return new Long(x).hashCode()*31 + new Long(y).hashCode();
				}
			}
		
			
			static class triplet implements Comparable<triplet>
			{
				Integer x,y,z;
				triplet(int x,int y,int z)
				{
					this.x = x;
					this.y = y;
					this.z = z;
				}
				
				public  int compareTo(triplet o)
				{
					int result = x.compareTo(o.x);
					if(result==0)
						result =  y.compareTo(o.y);
					if(result==0)
						result = z.compareTo(o.z);
	 
					return result;
				}
				
				public boolean equlas(Object o)
				{
					if(o instanceof triplet)
					{
						triplet p = (triplet)o;
						return x==p.x && y==p.y && z==p.z;
					}
					return false;
				}
				
				public String toString()
				{
					return x+" "+y+" "+z;
				}
				public int hashCode()
				{
					return new Long(x).hashCode()*31 + new Long(y).hashCode() + new Long(z).hashCode(); 
				}
			}
			
	 
			
			
	
		}