Problem Description

There is a positive integer $ N $ and powers of $ 2 $: $ 1, 2, 4, 8 $.

Among these, you can use the same power of $ 2 $ any number of times, to find one combination such that their sum equals $ N $. If there are multiple combinations, you may output any one of them.

For example, when $ N=5 $, since $ 5=1+2+2 $, one combination could be $ {1, 2, 2} $.

Input Format

The input is given from the standard input in the following format:

$ N $

• The first line contains a positive integer $N\ (1\ ≦\ N\ ≦\ 10)$.

Output Format

On the first line, output the number of integers $ K $ in the combination.

From the second line, output each of the $ K $ integers in the combination. The sum must exactly equal $ N $, and each integer must be a power of $ 2 $ to be considered correct. Otherwise, it will be considered incorrect.

Do not forget the newline at the end of the output.

Sample Input and Output

Sample Input #1

5

Sample Output #1

3
1
2
2

Sample Input #2

1

Sample Output #2

1
1

Notes/Hints

Sample Explanation 1

This is the example from the problem statement. Since $ 5=1+2+2 $, outputting this combination will be considered correct. Remember to output the number of integers in the combination first, which is $ 3 $. Alternatively, since $ 5=1+4 $, outputting the combination $ 1, 4 $ would also be correct.

见题面 Input 部分

见题面 Output 部分