lulu vs pano

The following two operations may be applied to a sequence consisting only of odd integers.

• Choose two elements $x,y$ at distinct positions in the current sequence. Let $G=\gcd(x,y)$. Remove $x,y$ from the sequence, then add $\cfrac{x}{G},\cfrac{y}{G},G$ to the sequence.
• Choose two elements $x,y$ at distinct positions in the current sequence. Remove $x,y$ from the sequence, then add $x\mathbin{\&}y$ to the sequence, where $\mathbin{\&}$ denotes bitwise AND.

You are given an integer $N$. Construct a sequence of length $N$ for which the minimum number of operations required to leave exactly one element equal to $1$ is exactly $N+3$.

The input is given in the following format.

$N$

On the first line, print the given length $N$ of the sequence.

On the second line, print the sequence elements $A_1,A_2,\cdots,A_N$, separated by spaces.

The printed sequence must satisfy all conditions in the statement. If there are multiple solutions, print any of them.

The output format is as follows.

$N$ $A_1\ A_2\ \cdots\ A_N$

• $3 \leq N \leq 10$.
• $1 \leq A_i \leq 2\,147\,483\,647$ ($1 \leq i \leq N$).
• Every $A_i$ is odd ($1 \leq i \leq N$).