Problem: You are given an array [a_1, a_2, ..., a_n] such that 1 ≤ a_i ≤ 10^9. Let S be the sum of all elements of the array a.

Let's call an array b of n integers beautiful if:

  * 1 ≤ b_i ≤ 10^9 for each i from 1 to n; 
  * for every pair of adjacent integers from the array (b_i, b_{i + 1}), either b_i divides b_{i + 1}, or b_{i + 1} divides b_i (or both); 
  * 2 ∑ _{i = 1}^{n} |a_i - b_i| ≤ S. 



Your task is to find any beautiful array. It can be shown that at least one beautiful array always exists.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of two lines. The first line contains one integer n (2 ≤ n ≤ 50).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9).

Output

For each test case, print the beautiful array b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^9) on a separate line. It can be shown that at least one beautiful array exists under these circumstances. If there are multiple answers, print any of them.

Example

Input


4
5
1 2 3 4 5
2
4 6
2
1 1000000000
6
3 4 8 1 2 3


Output


3 3 3 3 3
3 6
1 1000000000
4 4 8 1 3 3

Solution (in PYTHON3):

Solution:
import sys; import math; 
CASE=1; rla=''

inf=998244353535353535353

def solve() : 
    n=int(input()); li=[int(i) for i in input().split()]
    sum1=0; sum2=0; m=0
    for i in li : 
        if m==0 : sum1+=abs(1-i)
        else : sum2+=abs(1-i)
        m^=1
    if sum(li)>=2*sum1 : m=0
    else : m=1
    for i in li : 
        print(1 if m==0 else i, end=' ')
        m^=1
    print()

while True : 
    rla=sys.stdin.readline()
    cases=1
    if not rla: break
    if (rla=='\n')|(rla=='') : continue
    if CASE==1 : cases=int(rla)
    for cas in range(cases) : 
        
        solve()