human
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
The above is tricky. Write me a correct solution in PYTHON3.
 What is a Python program to find any value of d which yields a beautiful coloring, or report that it is impossible?
assistant
#Here is Python program to find any value of d which yields a beautiful coloring, or report that it is impossible.

import sys, collections, math, bisect, heapq, random, functools,io,os,copy
input = sys.stdin.readline
out = sys.stdout.flush
def rep():
    a = list(map(int,input().split()))
    return a

def sep():
    a = list(input().split())
    return a

class UnionFind:
    def __init__(self, x) -> None:
        self.uf = [-1] * x

    def find(self, x):
        r = x
        while self.uf[x] >= 0:
            x = self.uf[x]

        while r != x:
            self.uf[r], r = x, self.uf[r]
        return x

    def union(self, x, y):
        ux, uy = self.find(x), self.find(y)
        if ux == uy:
            return
        if self.uf[ux] >= self.uf[uy]:
            self.uf[uy] += self.uf[ux]
            self.uf[ux] = uy
        else:
            self.uf[ux] += self.uf[uy]
            self.uf[uy] = ux
        return

    def __print__(self):
        return self.uf

def spfa(x,g,n):
    dis = [float('inf') for i in range(n)]
    dis[x] = 0
    state = [False for i in range(n)]
    state[x] = True
    queue = collections.deque()
    queue.append(x)
    while queue:
        cur = queue.popleft()
        state[cur] = False
        for next_ in g[cur]:
            if dis[next_] > dis[cur] + 1:
                dis[next_] = dis[cur] + 1
                if state[next_] == False:
                    state[next_] = True
                    queue.append(next_)
    return dis

def gcd(x,y):
    if y == 0:
        return x
    return gcd(y,x % y)



def solve():
    n = int(input())
    a = rep()
    c1,c2 = a[0],a[1]
    for i in range(0,n,2):
        c1 = gcd(c1,a[i])
    for i in range(1,n,2):
        c2 = gcd(c2,a[i])
    if c1 == 1 and c2 == 1:
        print(0)
    else:
        flag = 1
        for i in range(1,n,2):
          if a[i] % c1 == 0:
             flag = 0
             break
        if flag:
          print(c1)

        else:
          flag2 = 1
          for i in range(0,n,2):
              if a[i] % c2 == 0:
                flag2 = 0
                break
          if flag2:
            print(c2)
         ...