13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5c0,

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.

Note

In the first sample, a

Game Bundles

Examples