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 os
import sys
from io import BytesIO, IOBase
from collections import Counter, defaultdict
import math
import heapq
import bisect
import collections
def ceil(a, b):
    return (a + b - 1) // b
BUFSIZE = 8192
inf = float('inf')
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)
get = lambda: sys.stdin.readline().rstrip("\r\n")
MOD = 1000000007
def v():
    return list()
# for _ in range(int(get())):
# n=int(get())
# l=list(map(int,get().split()))
# = map(int,get().split())
##################################################################################
def gcd(x, y):
    while (y):
        x, y = y, x % y
    return x
##################################################################################
for _ in range(int(get())):
    n = int(get())
    l = list(map(int, get().split()))
    g1=l[0]
    f1=0;f2=0
    for i in range(n):
        if i%2==0:
            g1=gcd(l[i],g1)
    for i in range(n):
        if i%2==1 and l[i]%g1==0:
            f1=1
            break
    g2=l[1]
    for i in range(n):
        if i%2==1:
            g2=gcd(l[i],g2)

    for i in range(n):
        if i%2==0 and l[i]%g2==0:
            f2=1
            break
    if f1==0:
        print(g1)
    elif f2==0:
        print(g2)
    else:
        f1=0;f2=0
        g=2
        for i in range(n):
            if i%2==0 and l[i]%2!=0:
                f1=1
                break
            if i%2==1 and l[i]%2==0:
                f1=1
                break

        for i in range(n):
            if i%2==1 and l[i]%2!=0:
                f2=1
                break
            if i%2==0 and l[i]%2==0:
                f2=1
                break
        if f1==0:
            print(2)
        elif f2==0:
            print(2)
        else:
            print(0)




