Read a positive natural number n. Generate and print, in lexicographic order, all decompositions of n as a sum of strictly increasing positive natural numbers (all terms are distinct, and on each line they are written in ascending order).
On the last line print the total number of decompositions found.
The program reads from standard input a single natural number, `n`. - `1 <= n <= 12` - A decomposition must have at least one term, so `n` itself is a valid decomposition (with a single term).
The program prints, one per line, all decompositions of `n` as a sum of strictly increasing positive integers. The terms of each decomposition are separated by spaces with no trailing space. Decompositions are printed in lexicographic order (those starting with smaller values come first). On the last line print the total number of decompositions.
6
1 2 3 1 5 2 4 6 4
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6
1 2 3 1 5 2 4 6 4
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