You are given an array a consisting of n positive integers. You have to choose a positive integer d and paint all elements into two colors. All elements which are divisible by d will be painted red, and all other elements will be painted blue.

The coloring is called beautiful if there are no pairs of adjacent elements with the same color in the array. Your task is to find any value of d which yields a beautiful coloring, or report that it is impossible.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

The first line of each testcase contains one integer n (2 ≤ n ≤ 100) — the number of elements of the array.

The second line of each testcase contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^{18}).

Output

For each testcase print a single integer. If there is no such value of d that yields a beautiful coloring, print 0. Otherwise, print any suitable value of d (1 ≤ d ≤ 10^{18}).

Example

Input


5
5
1 2 3 4 5
3
10 5 15
3
100 10 200
10
9 8 2 6 6 2 8 6 5 4
2
1 3


Output


2
0
100
0
3
1
5
6 5 12 5 16
 1
5
3 5 6 11 2

2
 0

import java.io.*;
import java.util.*;
import java.util.ArrayList;
import java.util.Arrays.*;
import java.util.Map.Entry;

import static java.util.Collections.*;
import static java.lang.Integer.parseInt;
import static java.lang.Math.*;
import static java.lang.String.format;
import static java.util.Arrays.*;

public class CC {
    static final int SCAN_LINE_LENGTH = 1_000_002;
    private static final boolean thread = false;
    @SuppressWarnings("all")
    static final boolean HAS_TEST_CASES = (1 == 1) ? true : false;

    @SuppressWarnings("all")
    private static ArrayList<Integer> adj[], v = new ArrayList<>();
    static long gcd = 1;
    static HashMap<Integer, Integer> pos;
    static int n, e[][], vis[], m, b[], a[];

    @SuppressWarnings("unchecked")
    static void solve() throws Exception {
        n = ni();
        long a[] = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nl();
        }
        ArrayList<Long> adj[] = new ArrayList[2];

        for (int i = 0; i < a.length; i++) {
            checkV(adj, i % 2);
            adj[i % 2].add(a[i]);
        }
        long gcd1 = adj[0].get(0), gcd2 = adj[1].get(0);
        for (int i = 1; i < adj[0].size(); i++) {
            gcd1 = gcd(gcd1, adj[0].get(i));
        }
        for (int i = 1; i < adj[1].size(); i++) {
            gcd2 = gcd(gcd2, adj[1].get(i));
        }

        boolean b1 = false, b2 = false;
        for (int i = 0; i < adj[0].size() && gcd2 != 1; i++) {
            if (adj[0].get(i) % gcd2 == 0) {
                b1 = true;
            }
        }
        for (int i = 0; i < adj[1].size() && gcd1 != 1; i++) {
            if (adj[1].get(i) % gcd1 == 0) {
                b2 = true;
            }
        }
        if (!b1 && gcd2 != 1) {
            pn(gcd2);
        } else if (!b2 && gcd1 != 1) {
            pn(gcd1);
        } else {
            pn(0);
        }
    }

    public static void main(final String[] args) throws Exception {
        if (!thread) {
            final int TEST_CASES = HAS_TEST_CASES ? ni() : 1;
            for (int i = 1; i <= TEST_CASES; i++) {
                // pni(i + " t");
                // out.print("Case #" + (i) + ": ");
                try {
                    solve();
                } catch (final Exception e) {
                    // pni("idk Exception");
                    // e.printStackTrace(System.err);
                    // System.exit(0);
                    throw e;
                }
            }
            out.flush();
        }
        r.close();
        out.close();
    }

    @SuppressWarnings("all")
    private static final int MOD = (int) (1e9 + 7), MOD_FFT = 998244353;
    private static final Reader r = new Reader();
    @SuppressWarnings("all")
    private static final int[][] GRID_DIRECTION_4 = { { 1, 0 }, { -1, 0 }, { 0, 1 }, { 0, -1 } };
    @SuppressWarnings("all")
    private static final int[][] GRID_DIRECTION_ALL = { { 1, 0 }, { -1, 0 }, { 0, 1 }, { 0, -1 }, { 1, 1 }, { -1, 1 },
            { 1, -1 }, { -1, -1 } };
    private static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    private static int[] deepCopy;

    public static long[] enumPows(int a, final int n, final int mod) {
        a %= mod;
        final long[] pows = new long[n + 1];
        pows[0] = 1;
        for (int i = 1; i <= n; i++)
            pows[i] = pows[i - 1] * a % mod;
        return pows;
    }

    @SuppressWarnings("all")
    private static ArrayList<Integer> sieve(final int n) {
        final ArrayList<Integer> p = new ArrayList<>();
        final int[] f = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            if (f[i] == 1)
                continue;
            for (int j = i * i; j <= n && j < f.length; j += i) {
                f[j] = 1;
            }
        }
        for (int i = 2; i < f.length; i++) {
            if (f[i] == 0)
                p.add(i);
        }
        return p;
    }

    @SuppressWarnings("all")
    private static void s(final int[] a) {
        final Integer[] t = new Integer[a.length];
        for (int i = 0; i < t.length; i++) {
            t[i] = a[i];
        }
        sort(t);
        for (int i = 0; i < t.length; i++) {
            a[i] = t[i];
        }
    }

    int pow(int a, int b, final int m) {
        int ans = 1;
        while (b != 0) {
            if ((b & 1) != 0)
                ans = (ans * a) % m;
            b /= 2;
            a = (a * a) % m;
        }
        return ans;
    }

    int modInverse(final int k) {
        return pow(k, MOD - 2, MOD);
    }

    @SuppressWarnings("all")
    private static void swap(final int i, final int j) {
        final int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    @SuppressWarnings("all")
    private static boolean isMulOverflow(final long A, final long B) {
        if (A == 0 || B == 0)
            return false;
        final long result = A * B;
        if (A == result / B)
            return true;
        return false;
    }

    @SuppressWarnings("all")
    private static int gcd(final int a, final int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    @SuppressWarnings("all")
    private static long gcd(final long a, final long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    @SuppressWarnings("all")
    private static class Pair<T, E> implements Comparable<Pair<T, E>> {
        T fir;
        E snd;

        Pair() {
        }

        Pair(final T x, final E y) {
            this.fir = x;
            this.snd = y;
        }

        /*
         * (non-Javadoc)
         * 
         * @see java.lang.Object#hashCode()
         */

        /*
         * (non-Javadoc)
         * 
         * @see java.lang.Object#toString()
         */

        @Override
        public String toString() {
            return "Pair [fir = " + fir + ", snd = " + snd + "]";
        }

        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + ((fir == null) ? 0 : fir.hashCode());
            result = prime * result + ((snd == null) ? 0 : snd.hashCode());
            return result;
        }

        /*
         * (non-Javadoc)
         * 
         * @see java.lang.Object#equals(java.lang.Object)
         */

        @Override
        public boolean equals(final Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            final Pair other = (Pair) obj;
            if (fir == null) {
                if (other.fir != null)
                    return false;
            } else if (!fir.equals(other.fir))
                return false;
            if (snd == null) {
                if (other.snd != null)
                    return false;
            } else if (!snd.equals(other.snd))
                return false;
            return true;
        }

        /**
         * @return the fir
         */
        public T getFir() {
            return fir;
        }

        /**
         * @param fir the fir to set
         */
        public void setFir(final T fir) {
            this.fir = fir;
        }

        /**
         * @return the snd
         */
        public E getSnd() {
            return snd;
        }

        /**
         * @param snd the snd to set
         */
        public void setSnd(final E snd) {
            this.snd = snd;
        }

        @Override
        @SuppressWarnings("unchecked")
        public int compareTo(final Pair<T, E> o) {
            final int c = ((Comparable<T>) fir).compareTo(o.fir);
            return c != 0 ? c : ((Comparable<E>) snd).compareTo(o.snd);
        }
        // @Override
        // @SuppressWarnings("unchecked")
        // public int compareTo(final Pair<T, E> o) {
        // final int c = ((Comparable<T>) fir).compareTo(o.fir);
        // return c;
        // }

    }

    @SuppressWarnings("all")
    private static class pi implements Comparable<pi> {
        int fir, snd;

        pi() {
        }

        pi(final int a, final int b) {
            fir = a;
            snd = b;
        }

        public int compareTo(final pi o) {
            return fir == o.fir ? snd - o.snd : fir - o.fir;
        }

        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + fir;
            result = prime * result + snd;
            return result;
        }

        @Override
        public boolean equals(final Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            final pi other = (pi) obj;
            if (fir != other.fir)
                return false;
            if (snd != other.snd)
                return false;
            return true;
        }

    }

    @SuppressWarnings("all")
    private static <T> void checkV(final Vector<T> adj[], final int i) {
        adj[i] = adj[i] == null ? new Vector<>() : adj[i];
    }

    @SuppressWarnings("all")
    private static <T> void checkV(final ArrayList<T> adj[], final int i) {
        adj[i] = adj[i] == null ? new ArrayList<>() : adj[i];
    }

    @SuppressWarnings("all")
    private static int[] na(final int n) throws Exception {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }

    @SuppressWarnings("all")
    private static int[] na1(final int n) throws Exception {
        final int[] a = new int[n + 1];
        for (int i = 1; i < a.length; i++) {
            a[i] = ni();
        }
        return a;
    }

    @SuppressWarnings("all")
    private static String n() throws IOException {
        return r.readToken();
    }

    @SuppressWarnings("all")
    private static char[] ns() throws IOException {
        return r.readToken().toCharArray();
    }

    @SuppressWarnings("all")
    private static String nln() throws IOException {
        return r.readLine();
    }

    private static int ni() throws IOException {
        return r.nextInt();
    }

    @SuppressWarnings("all")
    private static long nl() throws IOException {
        return r.nextLong();
    }

    @SuppressWarnings("all")
    private static double nd() throws IOException {
        return r.nextDouble();
    }

    @SuppressWarnings("all")
    private static void p(final Object o) {
        out.print(o);
    }

    @SuppressWarnings("all")
    private static void pn(final Object o) {
        out.println(o);
    }

    @SuppressWarnings("all")
    private static void pn() {
        out.println("");
    }

    @SuppressWarnings("all")
    private static void pi(final Object o) {
        out.print(o);
        out.flush();
    }

    @SuppressWarnings("all")
    private static void pni() {
        out.println("");
        out.flush();
    }

    private static void pni(final Object o) {
        out.println(o);
        out.flush();
    }

    private static class Reader {
        private final int BUFFER_SIZE = 1 << 17;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        // private StringTokenizer st;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        @SuppressWarnings("all")
        public Reader(final String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        final byte[] buf = new byte[SCAN_LINE_LENGTH];

        public String readLine() throws IOException {
            int cnt = 0;
            int c;
            o: while ((c = read()) != -1) {
                if (c == '\n')
                    if (cnt == 0)
                        continue o;
                    else
                        break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String readToken() throws IOException {
            int cnt = 0;
            int c;
            o: while ((c = read()) != -1) {
                if (!(c >= 33 && c <= 126))
                    if (cnt == 0)
                        continue o;
                    else
                        break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            final 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;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            final 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;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            final boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    // static {
    // if (thread)
    // new Thread(null, new Runnable() {
    // @Override
    // public void run() {
    // try {
    // final int testCases = HAS_TEST_CASES ? ni() : 1;
    // for (int i = 1; i <= testCases; i++) {
    // // out.print("Case #" + (i + 1) + ": ");
    // try {
    // solve();
    // } catch (final ArrayIndexOutOfBoundsException e) {
    // e.printStackTrace(System.err);
    // System.exit(-1);
    // } catch (final Exception e) {
    // pni("idk Exception in solve");
    // e.printStackTrace(System.err);
    // System.exit(-1);
    // }
    // }
    // out.flush();
    // } catch (final Throwable t) {
    // t.printStackTrace(System.err);
    // System.exit(-1);
    // }
    // }
    // }, "rec", (1L << 28)).start();
    // }

    @SuppressWarnings({ "all", })
    private static <T> T deepCopy(final T old) {
        try {
            return (T) deepCopyObject(old);
        } catch (final IOException | ClassNotFoundException e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
        return null;
    }

    private static Object deepCopyObject(final Object oldObj) throws IOException, ClassNotFoundException {
        ObjectOutputStream oos = null;
        ObjectInputStream ois = null;
        try {
            final ByteArrayOutputStream bos = new ByteArrayOutputStream(); // A
            oos = new ObjectOutputStream(bos); // B
            // serialize and pass the object
            oos.writeObject(oldObj); // C
            oos.flush(); // D
            final ByteArrayInputStream bin = new ByteArrayInputStream(bos.toByteArray()); // E
            ois = new ObjectInputStream(bin); // F
            // return the new object
            return ois.readObject(); // G
        } catch (final ClassNotFoundException e) {
            pni("Exception while Object Cloning = " + e);
            throw (e);
        } finally {
            oos.close();
            ois.close();
        }
    }

}