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.