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.BufferedOutputStream;
import java.io.Closeable;
import java.io.DataInputStream;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.AbstractCollection;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			long startTime = System.currentTimeMillis();
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			FastReader in = new FastReader(inputStream);
			Output out = new Output(outputStream);
			BWeakenedCommonDivisor solver = new BWeakenedCommonDivisor();
			solver.solve(1, in, out);
			out.close();
			System.err.println(System.currentTimeMillis()-startTime+"ms");
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<28);
		thread.start();
		thread.join();
	}

	static class BWeakenedCommonDivisor {
		ArrayList<Integer> primes = Utilities.sieve(44721);

		public BWeakenedCommonDivisor() {
		}

		public ArrayList<Integer> pf(int x) {
			ArrayList<Integer> ret = new ArrayList<>();
			for(int i: primes) {
				boolean valid = false;
				while(x%i==0) {
					valid = true;
					x /= i;
				}
				if(valid) {
					ret.add(i);
				}
			}
			if(x>1) {
				ret.add(x);
			}
			return ret;
		}

		public void solve(int kase, InputReader in, Output pw) {
			int n = in.nextInt()-1;
			HashSet<Integer> valid = new HashSet<>();
			valid.addAll(pf(in.nextInt()));
			valid.addAll(pf(in.nextInt()));
//			Utilities.Debug.dbg(valid);
			for(int i = 0; i<n; i++) {
				HashSet<Integer> nvalid = new HashSet<>();
				int a = in.nextInt(), b = in.nextInt();
				for(int j: valid) {
					if(a%j==0||b%j==0) {
						nvalid.add(j);
					}
				}
				valid = nvalid;
			}
			if(valid.isEmpty()) {
				pw.println(-1);
			}else {
				pw.println(valid.iterator().next());
			}
		}

	}

	static class Utilities {
		public static ArrayList<Integer> sieve(int n) {
			ArrayList<Integer> ans = new ArrayList<>();
			boolean[] prime = new boolean[n+1];
			Arrays.fill(prime, true);
			for(int i = 2; i<=n; i++) {
				if(prime[i]) {
					ans.add(i);
				}
				if((long) i*i>n) {
					continue;
				}
				for(int j = i*i; j<=n; j += i) {
					prime[j] = false;
				}
			}
			return ans;
		}

		public static class Debug {
			public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

			private static <T> String ts(T t) {
				if(t==null) {
					return "null";
				}
				try {
					return ts((Iterable) t);
				}catch(ClassCastException e) {
					if(t instanceof int[]) {
						String s = Arrays.toString((int[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof long[]) {
						String s = Arrays.toString((long[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof char[]) {
						String s = Arrays.toString((char[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof double[]) {
						String s = Arrays.toString((double[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof boolean[]) {
						String s = Arrays.toString((boolean[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}
					try {
						return ts((Object[]) t);
					}catch(ClassCastException e1) {
						return t.toString();
					}
				}
			}

			private static <T> String ts(T[] arr) {
				StringBuilder ret = new StringBuilder();
				ret.append("{");
				boolean first = true;
				for(T t: arr) {
					if(!first) {
						ret.append(", ");
					}
					first = false;
					ret.append(ts(t));
				}
				ret.append("}");
				return ret.toString();
			}

			private static <T> String ts(Iterable<T> iter) {
				StringBuilder ret = new StringBuilder();
				ret.append("{");
				boolean first = true;
				for(T t: iter) {
					if(!first) {
						ret.append(", ");
					}
					first = false;
					ret.append(ts(t));
				}
				ret.append("}");
				return ret.toString();
			}

			public static void dbg(Object... o) {
				if(LOCAL) {
					System.err.print("Line #"+Thread.currentThread().getStackTrace()[2].getLineNumber()+": [");
					for(int i = 0; i<o.length; i++) {
						if(i!=0) {
							System.err.print(", ");
						}
						System.err.print(ts(o[i]));
					}
					System.err.println("]");
				}
			}

		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public String lineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			lineSeparator = System.lineSeparator();
		}

		public void println(int i) {
			println(String.valueOf(i));
		}

		public void println(String s) {
			sb.append(s);
			println();
		}

		public void println() {
			sb.append(lineSeparator);
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}

	static interface InputReader {
		int nextInt();

	}

	static class FastReader implements InputReader {
		final private int BUFFER_SIZE = 1<<16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer;
		private int bytesRead;

		public FastReader(InputStream is) {
			din = new DataInputStream(is);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public int nextInt() {
			int ret = 0;
			byte c = skipToDigit();
			boolean neg = (c=='-');
			if(neg) {
				c = read();
			}
			do {
				ret = ret*10+c-'0';
			} while((c = read())>='0'&&c<='9');
			if(neg) {
				return -ret;
			}
			return ret;
		}

		private boolean isDigit(byte b) {
			return b>='0'&&b<='9';
		}

		private byte skipToDigit() {
			byte ret;
			while(!isDigit(ret = read())&&ret!='-') ;
			return ret;
		}

		private void fillBuffer() {
			try {
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			}catch(IOException e) {
				e.printStackTrace();
				throw new InputMismatchException();
			}
			if(bytesRead==-1) {
				buffer[0] = -1;
			}
		}

		private byte read() {
			if(bytesRead==-1) {
				throw new InputMismatchException();
			}else if(bufferPointer==bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

	}
}