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
#Fast
Give me a Python code to find any value of d which yields a beautiful coloring, or report that it is impossible?
assistant
#Here is Python code to find any value of d which yields a beautiful coloring, or report that it is impossible.
 I/O
import sys,os
import math
# To enable the file I/O i the below 2 lines are uncommented.
# read from in.txt if uncommented
if os.path.exists('in.txt'): sys.stdin=open('in.txt','r')
# will print on Console if file I/O is not activated
#if os.path.exists('out.txt'): sys.stdout=open('out.txt', 'w')
 
# inputs template
from io import BytesIO, IOBase
from heapq import *
from bisect import *
from collections import *

def main():
    for _ in range(mi()):
        x = mi()
        a = list(MI())
        if x == 1 : print(a[0]); continue
        eve = a[0]
        odd = a[1]
        for i in range(2,len(a)):
            if i&1:
                odd = math.gcd(odd,a[i])
            else:
                eve = math.gcd(eve,a[i])
        if eve == odd :
            print(0)
        else :
            flag1 = 0
            for i in range(0,len(a),2):
                if a[i]%odd == 0:
                    flag1 = 1
                    break
            flag2 = 0
            for i in range(1,len(a),2):
                if a[i]%eve == 0:
                    flag2 =1
                    break
            if flag1 and flag2:
                print(0)
            elif not flag2:
                print(eve)
            elif not flag1:
                print(odd)

# Sample Inputs/Output 
 
# 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,...