Sum#3888

Sum

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256 megabytes

Hard

You are given an integer $N$ and are asked to partition it into a sum of natural numbers (positive integers) so that the sum of the inverses of these natural numbers is equal to one. That is, find $K$ natural numbers $n_{1}, n_{2}, \dots, n_{K}$ n_1, n_2, \ldots, n_K such that

n_{1} + n_{2} + \dots + n_{K} = N

n_1 + n_2 + \ldots + n_K = N

and

\frac{1}{n _{1}} + \frac{1}{n _{2}} + \dots + \frac{1}{n _{K}} = 1.

\frac{1}{n_1} + \frac{1}{n_2} + \ldots + \frac{1}{n_K} = 1.

Input

The only input line contains the integer $N$ ( $1 \leq N \leq 1000000000$ 1 \leq N \leq 1000000000).

Output

If such a partition does not exist, output Epic fail on a single line. Otherwise, output the number of addends on the first line, and the addends themselves (in any order) on the second line. If there are several solutions, output any one of them.

Examples

Example 1

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n_{1}, n_{2}, \dots, n_{K}

n_{1} + n_{2} + \dots + n_{K} = N

\frac{1}{n _{1}} + \frac{1}{n _{2}} + \dots + \frac{1}{n _{K}} = 1.

1 \leq N \leq 1000000000