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Statement

 Goal

In number theory and combinatorics, an integer partition of a positive integer n is a way of expressing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition.

Write a program outputting all integer partitions of n in reverse lexicographic order. Each partition must satisfy the following conditions:

a1 + a2 + ... + ak = n
a1 ≥ a2 ≥ ... ≥ ak > 0

Output all integer partitions of n in reverse lexicographic order. The integers within each partition should be separated by spaces.
Input
An integer n.
Output
Multiple lines: each containing one partition.
Constraints
1 ≤ n ≤ 9
Example
Input
4
Output
4
3 1
2 2
2 1 1
1 1 1 1

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