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

# template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py

import os
import sys
from io import BytesIO, IOBase
import math
#from heapq import heappop, heappush, heapify
#from collections import deque
mod = 1000000007

def read():
    sys.stdin  = open('input.txt', 'r')  
    sys.stdout = open('output.txt', 'w') 

# ------------------------------------------- Algos --------------------------------------------------------
def sieve(n):
    prime = [True for i in range(n+1)]
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1
    return prime
def isPrime(n) : # Check Prime Number or not 
    if (n <= 1) : return False
    if (n <= 3) : return True
    if (n % 2 == 0 or n % 3 == 0) : return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True
def lower_bound(arr, n, k):
    start = 0
    end = n-1
    while start <= end:
        mid = (start+end)//2
        if arr[mid] == k:
            return mid
        elif arr[mid] > k:
            if mid > 0:
                if arr[mid-1] < k:
                    return (mid-1)
            else:
                return -1
        else:
            if mid < (n-1):
                if arr[mid+1] > k:
                    return mid
            else:
                return mid
def upper_bound(arr, n, k):
    start = 0
    end = n-1
    while start <= end:
        mid = (start+end)//2
        if arr[mid] == k:
            return mid
        elif arr[mid] > k:
            if mid > 0:
                if arr[mid-1] < k:
                    return (mid)
            else:
                return mid
        else:
            if mid < (n-1):
                if arr[mid+1] > k:
                    return (mid+1)
            else:
                return -1
def gcd(x, y):
    while y:
        x, y = y, x % y
    return x
 
def lcm(a,b):
    return (a // gcd(a,b))* b

# -------------------------------------------------- code -------------------------------------------------

def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        arr = list(map(int, input().split()))

        gcd1 = arr[0]
        for i in range(2, n, 2):
            gcd1 = gcd(gcd1, arr[i])

        gcd2 = arr[1]
        for i in range(3, n, 2):
            gcd2 = gcd(gcd2, arr[i])


        if gcd1 == gcd2:
            print(0)
            continue

        flag1 = True
        for i in range(0, n, 2):
            if arr[i] % gcd2 == 0:
                flag1 = False
                break

        flag2 = True
        for i in range(1, n, 2):
            if arr[i] % gcd1 == 0:
                flag2 = False
                break

        if flag1:
            print(gcd2)

        elif flag2:
            print(gcd1)

        else:
            print(0)
# ---------------------------------------------- region fastio ---------------------------------------------
BUFSIZE = 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")


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

# -------------------------------------------------- end region ---------------------------------------------

if __name__ == "__main__":
    #read()
    main()