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 sys
input = sys.stdin.readline
def mp():return map(int,input().split())
def lmp():return list(map(int,input().split()))
def mps(A):return [tuple(map(int, input().split())) for _ in range(A)]
import math
import bisect
import heapq
import time
from copy import copy as cc
from copy import deepcopy as dc
from itertools import accumulate
from collections import Counter, defaultdict, deque
def ceil(U,V):return (U+V-1)//V
def modf1(N,MOD):return (N-1)%MOD+1
inf = int(1e18+20)
mod = int(1e9+7)
from functools import reduce
def gcd(numbers):
    return reduce(math.gcd, numbers)

t = int(input())
for _ in range(t):
    n = int(input())
    a = lmp()
    odd = []
    even = []
    for i in range(n):
        if i % 2 == 0:
            odd.append(a[i])
        else:even.append(a[i])
    og = gcd(odd)
    eg = gcd(even)
    ans = 0
    flag = True
    for j in even:
        if j % og == 0:flag = False
    if flag:
        print(og)
        continue

    flag = True
    for j in odd:
        if j % eg == 0:flag = False
    if flag:
        ans = eg
        print(eg)
        continue
    print(0)

