Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Santa Claus and Candies

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSanta Claus has *n* candies, he dreams to give them as gifts to children.

What is the maximal number of children for whose he can give candies if Santa Claus want each kid should get distinct positive integer number of candies. Santa Class wants to give all *n* candies he has.

Input

The only line contains positive integer number *n* (1 ≤ *n* ≤ 1000) — number of candies Santa Claus has.

Output

Print to the first line integer number *k* — maximal number of kids which can get candies.

Print to the second line *k* distinct integer numbers: number of candies for each of *k* kid. The sum of *k* printed numbers should be exactly *n*.

If there are many solutions, print any of them.

Examples

Input

5

Output

2

2 3

Input

9

Output

3

3 5 1

Input

2

Output

1

2

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/22/2017 20:20:45 (p1).

Desktop version, switch to mobile version.
User lists

Name |
---|