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
import os
from math import ceil, floor, sqrt, gcd, factorial, log, log2
from io import BytesIO, IOBase
from collections import Counter, deque
# from itertools import permutations, combinations
from bisect import bisect
# from functools import reduce

inf=int(10e9)
BUFSIZE = 8192

inp = lambda: int(input())
mp = lambda: map(int, input().split())
lst = lambda: list(map(int, input().split()))


def main():
    for _ in range(inp()):
        n=inp()
        a=lst()
        u=0; v=0
        m1=10e20; m2=10e20

        for i in range(0, n, 2):
            if u==0:u=a[i]
            else:u=gcd(u, a[i])
            m1=min(m1, a[i])

        for i in range(1, n, 2):
            if v==0:v=a[i]
            else:v=gcd(v, a[i])
            m2=min(m2, a[i])

        if u%m1!=0 and v%m2!=0:
            print(0)
        else:
            fu=True
            fv=True
            for i in range(n):
                if i%2==0 and a[i]%m1==0:
                    continue
                elif i%2!=0 and a[i]%m1!=0:
                    continue
                else:
                    fu=False
                    break
            
            for i in range(n):
                if i%2==0 and a[i]%m2!=0:
                    continue
                elif i%2!=0 and a[i]%m2==0:
                    continue
                else:
                    fv=False
                    break
                    
            if fu: print(m1)
            elif fv:print(m2)
            else:print(0)
            






        # elif u%m1!=0:
        #     fv=True
        #     for i in range(0, n, 2):
        #         if a[i]%m2==0:
        #             fv=False
        #             break
        #     if fv:print(m2)
        #     else:print(0)
        # elif v%m2!=0:
        #     fu=True
        #     for i in range(1, n, 2):
        #         if a[i]%m1==0:
        #             fu=False
        #             break
        #     if fu:print(m1)
        #     else:print(0)
        # else:
        #     fu=True
        #     fv=True
        #     for i in range(1, n, 2):
        #         if a[i]%m1==0:
        #             fu=False
        #             break
        #     if fu:
        #         print(m1)
        #     else:
        #         for i in range(0, n, 2):
        #             if a[i]%m2==0:
        #                 fv=False
        #                 break
        #         if fv:
        #             print(m2)
        #         else:
        #             print(0)







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)
input = lambda: sys.stdin.readline().rstrip("\r\n")

if __name__ == "__main__":
    main()
