Santa Claus and Candies

Description:

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.

Sample Input:

5

Sample Output:

2
2 3

Sample Input:

9

Sample Output:

3
3 5 1

Sample Input:

2

Sample Output:

1
2