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 io, os
import sys 
from sys import stdin

from bisect import bisect_left, bisect_right
from collections import defaultdict, deque, namedtuple
from heapq import heappush, heappop
from math import gcd, ceil, floor, factorial, sqrt
from itertools import combinations, permutations

input = sys.stdin.buffer.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# input = sys.stdin.readline

def work():
    ans = 0 

    return 

# sys.setrecursionlimit(200010)
def main():
    test = int(input())

    for idt in range(test):
        n = int(input())
        # n, m = map(int, input().split())
        nums = list(map(int, input().split()))
        a, b = [], []
        for i in range(n):
            if i % 2 == 0:
                a.append(nums[i])
            else:
                b.append(nums[i])

        flag = False 
        for i in a:
            if i in b:
                flag = True 
                break 

        max_gcd1 = a[0]
        for i in range(1, len(a)):
            max_gcd1 = gcd(max_gcd1, a[i])

        max_gcd2 = b[0]
        for i in range(1, len(b)):
            max_gcd2 = gcd(max_gcd2, b[i])
        ans = 0 
        if max_gcd1 == max_gcd2 or flag:
            ans = 0 
        else:
            flag = True
            for i in b:
                if i % max_gcd1 == 0:
                    flag = False 
                    break 
            if flag:
                ans = max_gcd1 
            
            flag = True 
            for i in a:
                if i % max_gcd2 == 0:
                    flag = False 
                    break 
            if flag:
                ans = max_gcd2 
        print(ans)                 
            


    return 


if __name__ == '__main__':
    main()