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 os
import sys
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heapify, heappop, heappush, nlargest, nsmallest
from io import BytesIO, IOBase
from math import inf, sqrt
from types import GeneratorType

# Fast IO for Python

BUFSIZE: int = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
def input(): return sys.stdin.readline().rstrip("\r\n")


# Bootstrap used for recursion, use yield instead of return

def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
    return wrappedfunc


# Never use += for string concatenation
# Always use .join for string concatenation
# Use PyPy3 for Codeforces
# Use Python3 for Codechef

# Function to compute inverse of a under modulo m

def modInverse(a, m):

    g = gcd(a, m)

    if (g != 1):
        return -1

    else:
        # If a and m are relatively prime,
        # then modulo inverse is a^(m-2) mode m
        return power(a, m - 2, m)


# Function to compute x^y under modulo m

def power(x, y, m):

    if (y == 0):
        return 1

    p = power(x, y // 2, m) % m
    p = (p * p) % m

    if(y % 2 == 0):
        return p
    else:
        return ((x * p) % m)


# Function to return gcd of a and b

def gcd(a, b):
    if (a == 0):
        return b

    return gcd(b % a, a)


# Sieve of Eratosthenes to get prime upto n

def SieveOfEratosthenes(n):
    prime = [True for i in range(n+1)]
    p = 2
    while (p * p <= n):

        # If prime[p] is not
        # changed, then it is a prime
        if (prime[p] == True):

            # Update all multiples of p
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1

    ans = set()
    for p in range(2, n+1):
        if prime[p]:
            ans.add(p)

    return ans


MOD = 1000000007
INT_MAX = inf
INT_MIN = -inf


# Main function

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        a = list(map(int, input().split()))
        g1, g2 = a[0], a[1]
        for i in range(0, n, 2):
            g1 = gcd(g1, a[i])
        for i in range(1, n, 2):
            g2 = gcd(g2, a[i])

        if (g1 == 1 and g2 == 1) or g1 == g2:
            print(0)
        else:
            # if gcd(g1, g2) == 1:
            #     print(max(g1, g2))
            # else:
            #     print(0)

            if g2 > g1:
                check = False
                for i in range(0, n, 2):
                    if a[i] % g2 == 0:
                        check = True
                        break
                if check == True:
                    if g2 % g1 == 0:
                        print(0)
                    else:
                        check = False
                        for i in range(1, n, 2):
                            if a[i] % g1 == 0:
                                check = True
                                break
                        if check == True:
                            print(0)
                        else:
                            print(g1)

                else:
                    print(g2)

            else:
                check = False
                for i in range(1, n, 2):
                    if a[i] % g1 == 0:
                        check = True
                        break
                if check == True:
                    if g1 % g2 == 0:
                        print(0)
                    else:
                        check = False
                        for i in range(0, n, 2):
                            if a[i] % g2 == 0:
                                check = True
                                break
                        if check == True:
                            print(0)
                        else:
                            print(g2)
                else:
                    print(g1)


main()
