Selling pills

Kanguk sells pills, and he talks his customers into a purchase every time. One thing still bothers him.

Donggyu, a regular customer, orders some number of pills every day, anywhere from $1$ to $N$. Kanguk counted the pills out of the box one at a time, which took a while, and Donggyu lost his temper over the wait every time.

Kanguk worked out a faster way to hand the pills over. He splits the pills among several pouches and lines the pouches up in a row. When Donggyu asks for $k$ pills, Kanguk picks up one contiguous run of pouches whose pills add up to exactly $k$.

The counter holds at most $2000$ pouches in a row. Arrange the pouches so that Kanguk can serve any number from $1$ to $N$ that Donggyu calls out.

The first line contains $N$ ($1 \le N \le 10^6$), the largest number of pills Donggyu orders at once.

Print the number of pouches $K$ ($1 \le K \le 2000$) on the first line. On the second line print the number of pills in each pouch from left to right, separated by single spaces. Every pouch holds between $1$ and $10^6$ pills, and every number from $1$ to $N$ is the sum of some contiguous run of pouches.

Many arrangements satisfy those conditions, so the judge accepts only the arrangement built by the following rule.

• Let $b$ be the smallest positive integer with $b^2 \ge N$.
• Let $c = \lceil N / b \rceil$.
• Then $K = (b - 1) + c$. Starting from the left, place $b - 1$ pouches holding $1$ pill each, then $c$ pouches holding $b$ pills each.