#P1854E. Game Bundles

Game Bundles

Description

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 6060.

Your task is to choose kk games, where 1k601 \leq k \leq 60, along with their respective enjoyment values a1,a2,,aka_1, a_2, \dots, a_k, in such a way that exactly mm distinct game bundles can be formed.

The input is a single integer mm (1m10101 \le m \le 10^{10}) — the desired number of game bundles.

The first line should contain an integer kk (1k601 \le k \le 60) — the number of games.

The second line should contain kk integers, a1,a2,,aka_1, a_2, \dots, a_k (1a1,a2,,ak601 \le a_1, a_2, \dots, a_k \le 60) — the enjoyment values of the kk games.

Input

The input is a single integer mm (1m10101 \le m \le 10^{10}) — the desired number of game bundles.

Output

The first line should contain an integer kk (1k601 \le k \le 60) — the number of games.

The second line should contain kk integers, a1,a2,,aka_1, a_2, \dots, a_k (1a1,a2,,ak601 \le a_1, a_2, \dots, a_k \le 60) — the enjoyment values of the kk games.

样例输入 1

4

样例输出 1

4
20 20 20 20

样例输入 2

722

样例输出 2

15
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

样例输入 3

1

样例输出 3

1
60

Note

In the first sample, any subset of size 33 is a game bundle. There are 44 such subsets.