_E.Space_ had a dream.

He dreamt about a magic sequence. Someone had told him that this sequence was closely related to the examination tomorrow. He made up his mind to memorize it.

However, after waking up, _E.Space_ found that he had forgot that magic sequence; but fortunately, he remembered that the sequence has an interesting property.

In the dream, _E.Space_ applied to the sequence a series of operations.

The sequence was denoted by $a_1,a_2,\cdots,a_n$. Initially, $\forall~1\le i \le n$, $a_i\ge0$ and $a_n\ne 0$.

Later on, _E.Space_ chose an $i$ satisfying $a_i=i$ during each operation, setting $a_i$ to $0$, and increasing $a_1,a_2,\cdots,a_{i-1}$ by $1$, respectively.

_E.Space_ remembers that, after $n+k$ operations, the sequence had been transformed into a zero sequence, that is, $a_1=a_2=\cdots=a_n=0$.

He knows that there may be multiple sequences satisfying that property, but he still wishes you to tell him a possible one. You never know, all sequences like that work in the exam.

His grade is now in charge of you.

Input Format

One line, a positive integer $k$.

Output Format

If you find any sequences with the property _E.Space_ described above, output two lines.

On the first line, output a positive integer $n$.

On the second line, print $n$ nonnegative integers, $a_1,a_2,\cdots,a_n$, where $a_n\ne 0$, denoting one possible magic sequence.

If there exist multiple ones, print any.

If there is no possible sequence, output one line, including only a string Daydream!, to tell _E.Space_ that he had a daydream.

Sample

Input

1

Output

2
1 2

Sample

Input

5

Output

4
1 2 2 4

Subtasks

Subtask 1 (10 points): $k\le 6$.

Subtask 2 (25 points): $k\le 10^6$.

Subtask 3 (30 points): $k\le 10^{11}$, and it is guaranteed that there is a solution satisfying $\forall 1\le i < n,~a_i\ne i$, if any solution exists.

Subtask 4 (28 points): $k\le 10^{11}.$

Subtask 5 (7 points): $k\le 10^{12}$.