E. Game Bundles
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Rishi is developing games in the 2D metaverse and wants to offer game bundles to his customers. Each game has an associated enjoyment value. A game bundle consists of a subset of games whose total enjoyment value adds up to $$$60$$$.

Your task is to choose $$$k$$$ games, where $$$1 \leq k \leq 60$$$, along with their respective enjoyment values $$$a_1, a_2, \dots, a_k$$$, in such a way that exactly $$$m$$$ distinct game bundles can be formed.

Input

The input is a single integer $$$m$$$ ($$$1 \le m \le 10^{10}$$$) — the desired number of game bundles.

Output

The first line should contain an integer $$$k$$$ ($$$1 \le k \le 60$$$) — the number of games.

The second line should contain $$$k$$$ integers, $$$a_1, a_2, \dots, a_k$$$ ($$$1 \le a_1, a_2, \dots, a_k \le 60$$$) — the enjoyment values of the $$$k$$$ games.

Examples
Input
4
Output
4
20 20 20 20
Input
722
Output
15
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Input
1
Output
1
60
Note

In the first sample, any subset of size $$$3$$$ is a game bundle. There are $$$4$$$ such subsets.