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.*;

public class Main {

    static class Pair {
        int l, r;

        public Pair(int l, int r) {
            this.l = l;
            this.r = r;
        }
    }

    static long mod = (long) 1e9 + 7;

    public static final double PI = 3.141592653589793d;

    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC
    {
        public static void solve(int testNumber, InputReader in, OutputWriter out)
        {
            int t=in.readInt();
            while(t-->0)
            {
                int n=in.readInt();
                long arr[]=new long[n];
                for(int i=0;i<n;++i)
                {
                    arr[i]=in.nextLong();
                }
                long gcd1=arr[0],gcd2=arr[1],last=arr[0];
                for(int i=2;i<n;i+=2)
                {
                    gcd1=CP.gcd(last,arr[i]);
                    last=gcd1;
                }
                last=arr[1];
                for(int i=1;i<n;i+=2)
                {
                    gcd2=CP.gcd(last,arr[i]);
                    last=gcd2;
                }
                //out.printLine(gcd1+" "+gcd2);
                long flag=1;
                if(gcd1==gcd2)
                {
                    out.printLine(0);
                }
                else if(gcd2>gcd1)
                {
                    for(int i=0;i<n;i+=2)
                    {
                        if(arr[i]%gcd2==0)
                        {
                            flag=0;
                            break;
                        }
                    }
                    if(flag==0)
                    {
                        out.printLine(0);
                    }
                    else
                    {
                        out.printLine(gcd2);
                    }
                }
                else
                {
                    for(int i=1;i<n;i+=2)
                    {
                        if(arr[i]%gcd1==0)
                        {
                            flag=0;
                            break;
                        }
                    }
                    if(flag==0)
                    {
                        out.printLine(0);
                    }
                    else
                    {
                        out.printLine(gcd1);
                    }
                }
            }
        }
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int arraySize) {
            int[] array = new int[arraySize];

            for (int i = 0; i < arraySize; i++) {
                array[i] = readInt();
            }

            return array;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isNewLine(int c) {
            return c == '\n';
        }

        public String nextLine() {
            int c = read();

            StringBuilder result = new StringBuilder();

            do {
                result.appendCodePoint(c);

                c = read();
            } while (!isNewLine(c));

            return result.toString();
        }

        public long nextLong() {
            int c = read();

            while (isSpaceChar(c)) {
                c = read();
            }

            int sign = 1;

            if (c == '-') {
                sign = -1;

                c = read();
            }

            long result = 0;

            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }

                result *= 10;
                result += c & 15;

                c = read();
            } while (!isSpaceChar(c));

            return result * sign;
        }

        public long[] nextLongArray(int arraySize) {
            long array[] = new long[arraySize];

            for (int i = 0; i < arraySize; i++) {
                array[i] = nextLong();
            }

            return array;
        }

        public double nextDouble() {
            double ret = 0, div = 1;
            byte c = (byte) read();

            while (c <= ' ') {
                c = (byte) read();
            }

            boolean neg = (c == '-');

            if (neg) {
                c = (byte) read();
            }

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

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

            if (neg) {
                return -ret;
            }

            return ret;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }
    }

    static class CP {

        static boolean isPrime(long n) {
            if (n <= 1)
                return false;
            if (n == 2 || n == 3)
                return true;
            if (n % 2 == 0 || n % 3 == 0)
                return false;
            for (int i = 5; (long) i * i <= n; i += 6) {
                if (n % i == 0 || n % (i + 2) == 0)
                    return false;
            }
            return true;
        }

        static String addChar(String s, int n, String ch) {
            String res = s + String.join("", Collections.nCopies(n, ch));
            return res;
        }

        static int ifnotPrime(int[] prime, int x) {

            return (prime[x / 64] & (1 << ((x >> 1) & 31)));
        }

        static int log2(long n) {
            return (int) (Math.log10(n) / Math.log10(2));
        }

        static void makeComposite(int[] prime, int x) {

            prime[x / 64] |= (1 << ((x >> 1) & 31));
        }

        static ArrayList<Integer> bitWiseSieve(int n) {
            ArrayList<Integer> al = new ArrayList<>();
            int prime[] = new int[n / 64 + 1];


            for (int i = 3; i * i <= n; i += 2) {

                if (ifnotPrime(prime, i) == 0)
                    for (int j = i * i, k = i << 1;
                         j < n; j += k)
                        makeComposite(prime, j);
            }

            al.add(2);

            for (int i = 3; i <= n; i += 2)
                if (ifnotPrime(prime, i) == 0)
                    al.add(i);

            return al;
        }

        public static long[] sort(long arr[]) {
            List<Long> list = new ArrayList<>();
            for (long n : arr) {
                list.add(n);
            }
            Collections.sort(list);
            for (int i = 0; i < arr.length; i++) {
                arr[i] = list.get(i);
            }
            return arr;
        }


        static ArrayList<Integer> sieve(long size) {

            ArrayList<Integer> pr = new ArrayList<Integer>();
            boolean prime[] = new boolean[(int) size];
            for (int i = 2; i < prime.length; i++) prime[i] = true;
            for (int i = 2; i * i < prime.length; i++) {
                if (prime[i]) {
                    for (int j = i * i; j < prime.length; j += i) {
                        prime[j] = false;
                    }
                }
            }
            for (int i = 2; i < prime.length; i++) if (prime[i]) pr.add(i);
            return pr;
        }

        static ArrayList<Integer> segmented_sieve(int l, int r, ArrayList<Integer> primes) {
            ArrayList<Integer> al = new ArrayList<>();
            if (l == 1) ++l;
            int max = r - l + 1;
            int arr[] = new int[max];
            for (int p : primes) {
                if (p * p <= r) {
                    int i = (l / p) * p;
                    if (i < l) i += p;
                    for (; i <= r; i += p) {
                        if (i != p) {
                            arr[i - l] = 1;
                        }
                    }
                }
            }
            for (int i = 0; i < max; ++i) {
                if (arr[i] == 0) {
                    al.add(l + i);
                }
            }
            return al;
        }

        static boolean isfPrime(long n, int iteration) {

            if (n == 0 || n == 1)
                return false;

            if (n == 2)
                return true;

            if (n % 2 == 0)
                return false;

            Random rand = new Random();
            for (int i = 0; i < iteration; i++) {
                long r = Math.abs(rand.nextLong());
                long a = r % (n - 1) + 1;
                if (modPow(a, n - 1, n) != 1)
                    return false;
            }
            return true;
        }

        static long modPow(long a, long b, long c) {
            long res = 1;
            for (int i = 0; i < b; i++) {
                res *= a;
                res %= c;
            }
            return res % c;
        }

        private static long binPower(long a, long l, long mod) {

            long res = 0;

            while (l > 0) {
                if ((l & 1) == 1) {
                    res = mulmod(res, a, mod);
                    ;
                    l >>= 1;
                }
                a = mulmod(a, a, mod);
            }
            return res;
        }

        private static long mulmod(long a, long b, long c) {

            long x = 0, y = a % c;
            while (b > 0) {
                if (b % 2 == 1) {
                    x = (x + y) % c;
                }
                y = (y * 2L) % c;
                b /= 2;
            }
            return x % c;

        }

        static long binary_Expo(long a, long b) {
            long res = 1;
            while (b != 0) {
                if ((b & 1) == 1) {
                    res *= a;
                    --b;
                }
                a *= a;
                b /= 2;
            }
            return res;
        }

        static long Modular_Expo(long a, long b) {
            long res = 1;
            while (b != 0) {
                if ((b & 1) == 1) {
                    res = (res * a) % 1000000007;
                    --b;
                }
                a = (a * a) % 1000000007;
                b /= 2;
            }
            return res % 1000000007;
        }

        static int i_gcd(int a, int b) {
            while (true) {
                if (b == 0)
                    return a;
                int c = a;
                a = b;
                b = c % b;
            }
        }

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

        static long ceil_div(long a, long b) {
            return (a + b - 1) / b;
        }

        static int getIthBitFromInt(int bits, int i) {
            return (bits >> (i - 1)) & 1;
        }

        private static TreeMap<Long, Long> primeFactorize(long n) {
            TreeMap<Long, Long> pf = new TreeMap<>(Collections.reverseOrder());
            long cnt = 0;
            long total = 1;
            for (long i = 2; (long) i * i <= n; ++i) {
                if (n % i == 0) {
                    cnt = 0;
                    while (n % i == 0) {
                        ++cnt;
                        n /= i;
                    }
                    pf.put(cnt, i);
                    //total*=(cnt+1);
                }
            }
            if (n > 1) {
                pf.put(1L, n);
                //total*=2;
            }
            return pf;
        }

        static long upper_Bound(long a[], long x) {
            long l = -1, r = a.length;
            while (l + 1 < r) {
                long m = (l + r) >>> 1;
                if (a[(int) m] <= x)
                    l = m;
                else
                    r = m;
            }
            return l + 1;
        }

        static int lower_Bound(ArrayList<Integer> a, int x) {
            int l = 0, r = a.size() - 1, ans = -1, mid = 0;
            while (l <= r) {
                mid = (l + r) >> 1;
                if (a.get(mid) <= x) {
                    ans = mid;
                    l = mid + 1;
                } else {
                    r = mid - 1;
                }
            }
            return ans;
        }

        static long lower_Bound(long a[], long x) {
            int l = -1, r = a.length;
            while (l + 1 < r) {
                int m = (l + r) >>> 1;
                if (a[(int) m] >= x)
                    r = m;
                else
                    l = m;
            }
            return (long) r;
        }

        static int upperBound(int a[], int x) {// x is the key or target value
            int l = -1, r = a.length;
            while (l + 1 < r) {
                int m = (l + r) >>> 1;
                if (a[m] <= x) l = m;
                else r = m;
            }
            return l + 1;
        }

        static int bsh(int a[], int t) {
            int ans = -1;
            int i = 0, j = a.length - 1;
            while (i <= j) {
                int mid = i + (j - i) / 2;
                if (a[mid] > t) {
                    ans = mid;
                    //System.out.print("uppr "+a[ans]);
                    j = mid - 1;
                } else {
                    //System.out.print("less "+a[mid]);
                    i = mid + 1;
                }
            }
            return ans;
        }

        static int bsl(int a[], int t) {
            int ans = -1;
            int i = 0, j = a.length - 1;
            while (i <= j) {
                int mid = i + (j - i) / 2;
                if (a[mid] <= t) {
                    ans = mid;
                    i = mid + 1;
                } else if (a[mid] > t) {
                    j = mid - 1;
                }
            }
            return ans;
        }

        static int upper_Bound(ArrayList<Integer> a, int x)  //closest to the right
        {
            int l = 0, r = a.size() - 1, ans = -1, mid = 0;
            while (l <= r) {
                mid = (l + r) >> 1;
                if (a.get(mid) > x) {
                    ans = mid;
                    r = mid - 1;
                } else {
                    l = mid + 1;
                }
            }
            return ans;
        }

        static boolean isSquarefactor(int x, int factor, int target) {
            int s = (int) Math.round(Math.sqrt(x));
            return factor * s * s == target;
        }

        static boolean isSquare(int x) {
            int s = (int) Math.round(Math.sqrt(x));
            return x * x == s;
        }

        static void sort(int a[]) // heap sort
        {
            PriorityQueue<Integer> q = new PriorityQueue<>();
            for (int i = 0; i < a.length; i++)
                q.add(a[i]);
            for (int i = 0; i < a.length; i++)
                a[i] = q.poll();
        }

        static void shuffle(int[] in) {
            for (int i = 0; i < in.length; i++) {
                int idx = (int) (Math.random() * in.length);
                fast_swap(in, idx, i);
            }
        }

        static boolean isPalindrome(String s) {
            StringBuilder sb = new StringBuilder(s);
            sb.reverse();
            if (s.equals(sb.toString())) {
                return true;
            }
            return false;
        }

        static int[] computeLps(String pat) {
            int len = 0, i = 1, m = pat.length();
            int lps[] = new int[m];
            lps[0] = 0;
            while (i < m) {
                if (pat.charAt(i) == pat.charAt(len)) {
                    ++len;
                    lps[i] = len;
                    ++i;
                } else {
                    if (len != 0) {
                        len = lps[len - 1];
                    } else {
                        lps[i] = len;
                        ++i;
                    }
                }
            }
            return lps;
        }

        static void kmp(String s, String pat, int[] prf, int[] st) {
            int n = s.length(), m = pat.length();
            int lps[] = computeLps(pat);
            int i = 0, j = 0;
            while (i < n) {
                if (s.charAt(i) == pat.charAt(j)) {
                    i++;
                    j++;
                    if (j == m) {
                        ++prf[(i - j) + m];
                        ++st[(i - j) + 1];
                        j = lps[j - 1];
                    }

                } else {
                    if (j != 0) {
                        j = lps[j - 1];
                    } else {
                        i++;
                    }
                }
            }
        }

        static void reverse_ruffle_sort(int a[]) {
            shuffle(a);
            Arrays.sort(a);
            for (int l = 0, r = a.length - 1; l < r; ++l, --r)
                fast_swap(a, l, r);

        }

        static void ruffle_sort(int a[]) {
            shuffle(a);
            Arrays.sort(a);
        }

        static int getMax(int arr[], int n) {
            int mx = arr[0];
            for (int i = 1; i < n; i++)
                if (arr[i] > mx)
                    mx = arr[i];
            return mx;
        }

        static ArrayList<Long> primeFactors(long n) {
            ArrayList<Long> al = new ArrayList<>();
            al.add(1L);
            while (n % 2 == 0) {
                if (!al.contains(2L)) {
                    al.add(2L);
                }
                n /= 2L;
            }

            for (int i = 3; (long) i * i <= n; i += 2) {
                while ((n % i == 0)) {
                    if (!al.contains((long) i)) {
                        al.add((long) i);
                    }
                    n /= i;
                }
            }

            if (n > 2) {
                if (!al.contains(n)) {
                    al.add(n);
                }
            }
            return al;
        }

        static int[] z_function(String s) {
            int n = s.length(), z[] = new int[n];

            for (int i = 1, l = 0, r = 0; i < n; ++i) {
                if (i <= r)
                    z[i] = Math.min(z[i - l], r - i + 1);

                while (i + z[i] < n && s.charAt(z[i]) == s.charAt(i + z[i]))
                    ++z[i];

                if (i + z[i] - 1 > r) {
                    l = i;
                    r = i + z[i] - 1;
                }
            }
            return z;
        }


        static void fast_swap(int[] a, int idx1, int idx2) {
            if (a[idx1] == a[idx2])
                return;

            a[idx1] ^= a[idx2];
            a[idx2] ^= a[idx1];
            a[idx1] ^= a[idx2];
        }

        public static void fast_sort(long[] array) {
            ArrayList<Long> copy = new ArrayList<>();
            for (long i : array)
                copy.add(i);
            Collections.sort(copy);
            for (int i = 0; i < array.length; i++)
                array[i] = copy.get(i);
        }

        static int divCount(int n) {
            boolean hash[] = new boolean[n + 1];
            Arrays.fill(hash, true);
            for (int p = 2; p * p < n; p++)
                if (hash[p] == true)
                    for (int i = p * 2; i < n; i += p)
                        hash[i] = false;

            int total = 1;
            for (int p = 2; p <= n; p++) {
                if (hash[p]) {
                    int count = 0;
                    if (n % p == 0) {
                        while (n % p == 0) {
                            n = n / p;
                            count++;
                        }
                        total = total * (count + 1);
                    }
                }
            }
            return total;
        }

        static long binomialCoeff(long n, long k) {
            long res = 1;

            if (k > n - k)
                k = n - k;

            for (int i = 0; i < k; ++i) {
                res = (res * (n - i));
                res /= (i + 1);
            }
            return res;
        }

        static long c(long fact[], long n, long k) {
            if (k > n) return 0;
            long res = fact[(int) n];
            res = (int) ((res * Modular_Expo(fact[(int) k], mod - 2)) % mod);
            res = (int) ((res * Modular_Expo(fact[(int) n - (int) k], mod - 2)) % mod);
            return res % mod;
        }

        public static ArrayList<Long> getFact(long x) {

            ArrayList<Long> facts = new ArrayList<>();
            for (long i = 2; i * i <= x; ++i) {
                if (x % i == 0) {
                    facts.add(i);
                    if (i != x / i) {
                        facts.add(x / i);
                    }
                }
            }
            return facts;
        }

        static void matrix_ex(long n, long[][] A, long[][] I) {
            while (n > 0) {
                if (n % 2 == 0) {
                    Multiply(A, A);
                    n /= 2;
                } else {
                    Multiply(I, A);
                    n--;
                }
            }
        }

        static void Multiply(long[][] A, long[][] B) {

            int n = A.length, m = A[0].length, p = B[0].length;

            long[][] C = new long[n][p];

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < p; j++) {
                    for (int k = 0; k < m; k++) {
                        C[i][j] += ((A[i][k] % mod) * (B[k][j] % mod)) % mod;
                        C[i][j] = C[i][j] % mod;
                    }
                }
            }

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < p; j++) {
                    A[i][j] = C[i][j];
                }
            }
        }

        public static HashMap<Integer, Integer> sortMap(HashMap<Integer, Integer> map) {

            List<Map.Entry<Integer, Integer>> list = new LinkedList<>(map.entrySet());

            Collections.sort(list, (o1, o2) -> o2.getValue() - o1.getValue());

            HashMap<Integer, Integer> temp = new LinkedHashMap<>();

            for (Map.Entry<Integer, Integer> i : list) {
                temp.put(i.getKey(), i.getValue());
            }
            return temp;
        }

        public static long lcm(long l, long l2) {

            long val = CP.gcd(l, l2);
            return (l * l2) / val;

        }
    }

    static void py() {
        System.out.println("YES");
    }

    static void pn() {
        System.out.println("NO");
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void printLine(int[] array) {
            print(array);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

        public void printLine(int i) {
            writer.println(i);
        }

        public void printLine(char c) {
            writer.println(c);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }
    }
}




