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 static java.lang.Math.*;

public class cfs505B {
    static final int maxPrime = 44730; // ceil(sqrt ( 2 * 10^9 ))
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        StringBuilder sb = new StringBuilder();
        int n = sc.nextInt();
        long[] nums = sc.readLongArray(2*n);
        List<Long> primeList = new ArrayList<Long>();
        {
            int[] primes = generatePrimes(maxPrime);
            // add unique factors numbers between pair to frequency
            List<Long> factor1 = factor(primes, nums[0]);
            List<Long> factor2 = factor(primes, nums[1]);
            HashSet<Long> seen = new HashSet<Long>();
            for (Long l : factor1) {
                seen.add(l);
            }
            for (Long l : factor2) {
                seen.add(l);
            }
            for (Long l : seen) {
                primeList.add(l);
            }
        }
        Map<Long, Integer> freq = new HashMap<Long, Integer>();
        for (int i = 0; i < n; i++) {
            for (int primeIndex = 0; primeIndex < primeList.size(); primeIndex++) { // try to cut this down
                long p = primeList.get(primeIndex);
                boolean added = false;
                while (nums[2*i]%p == 0) {
                    nums[2*i] /= p;
                    added = true;
                }
                while (nums[2*i+1]%p == 0) {
                    nums[2*i+1] /= p;
                    added = true;
                }
                if (added) {
                    long prime = p;
                    Integer k  = freq.get(prime);
                    freq.put(prime, k == null ? 1 : k + 1);
                }
            }
        }
        for (Map.Entry<Long, Integer> entry : freq.entrySet()) {
            if (entry.getValue() == n) {
                System.out.println(entry.getKey());
                return;
            }
        }
        System.out.println(-1);



        System.out.print(sb);
    }
    /* returns boolean array a[] such that a[p] == true iff p is prime. */
    static boolean [] sieve(int N) {
        boolean [] a = new boolean[N+1];
        Arrays.fill(a, true);
        a[0] = a[1] = false;
        for (int p = 2; p * p <= N; p++)
            if (a[p]) {
                // Iterate through all multiples m of the prime and mark
                // them as not prime.
                for (int m = p * p; m <= N; m += p)
                    a[m] = false;
            }
        return a;
    }

    /* generate all prime numbers from 2..N, inclusive */
    static int [] generatePrimes(int N) {
        List<Integer> primes = new ArrayList<Integer>();
        boolean [] isPrime = sieve(N);
        for (int i = 0; i <= N; i++)
            if (isPrime[i])
                primes.add(i);
        int [] pa = new int[primes.size()];
        for (int i = 0; i < pa.length; i++)
            pa[i] = primes.get(i);
        return pa;
    }

    /*
     * P - list of primes
     * n - number to factor
     * @return list of prime factors, e.g. n = 100 returns [2, 2, 5, 5]
     */
    static List<Long> factor(int []P, long n) {
        List<Long> result = new ArrayList<Long>();
        for (int i = 0; i < P.length; i++) {
            long p = P[i];
            if (p * p > n) break;
            while (n % p == 0) {
                result.add(p);
                n /= p;
            }
        }
        if (n != 1) // large prime remainder
            result.add(n);

        return result;
    }


    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextLong();
            }
            return a;
        }
    }
}