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.*;
import java.util.*;

public class tr {
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int n=sc.nextInt();
		boolean []se=new boolean [100001];
		ArrayList <Integer> primes=new ArrayList();
		Arrays.fill(se, true);
		se[0]=se[1]=false;
		op []pp=new op[n];
		for(int i=0;i<n;i++) {
			pp[i]=new op(sc.nextInt(),sc.nextInt());
		}
		if(n==1) {
			System.out.println(pp[0].a);
			return;
		}
		int n1=pp[0].a;
		int n2=pp[0].b;
		for(int i=2;i<se.length;i++) {
			if(se[i]) {
				primes.add(i);
				if(1l * i * i <= 100000)
					for (int j = i * i; j < se.length; j += i)
					      se[j] =true;
			}
		} 
		HashSet<Integer>factors=new HashSet<>();		//take abs(N) in case of -ve integers
		int idx = 0, p = primes.get(idx);
		while(p * p <= n1)
		{
			while(n1 % p == 0) { factors.add(p); n1 /= p; }
			p = primes.get(++idx);
		}

		if(n1 != 1)						// last prime factor may be > sqrt(N)
			factors.add(n1);	
		idx = 0;
		p = primes.get(idx);
		while(p * p <= n2)
		{
			while(n2 % p == 0) { factors.add(p); n2 /= p; }
			p = primes.get(++idx);
		}

		if(n2 != 1)						// last prime factor may be > sqrt(N)
			factors.add(n2);
		boolean ans=false;
		int aa=0;
		for(int h:factors) {
			boolean acc=true;
			for(int i=1;i<n;i++) {
				if(pp[i].a%h!=0 && pp[i].b%h!=0) {
					acc=false;
					break;
				}
			}
			if(acc) {
				aa=h;
				ans=true;
				break;
			}
		}
		//out.println(factors);
	   if(ans)
		   out.println(aa);
	   else
		   out.println(-1);
		out.flush();
	}

	static int tryy(int[] a) {
		if (a.length == 1)
			return 1;
		if (issorted(a))
			return a.length;
		int[] a1 = new int[a.length / 2];
		int[] a2 = new int[a.length / 2];
		int j = 0;
		for (int i = 0; i < a.length; i++) {
			if (i < a.length / 2)
				a1[i] = a[i];
			else {
				a2[j++] = a[i];
			}
		}
		if (issorted(a1) || issorted(a2))
			return a1.length;
		return Math.max(tryy(a1), tryy(a2));
	}

	static boolean issorted(int[] a) {
		for (int i = 0; i < a.length - 1; i++)
			if (a[i] > a[i + 1])
				return false;
		// System.out.println(Arrays.toString(a));
		return true;
	}

	static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	static class op {
		int a;
		int b;

		op(int a, int b) {
			this.a = a;
			this.b = b;
		}

		public String toString() {
			return a + " " + b;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}