13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6cf,

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

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

$$$1 \le b_i \le 10^9$$$ 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);
$$$2 \sum \limits_{i = 1}^{n} |a_i - b_i| \le S$$$.

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 $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

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

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10

Find The Array

Examples