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Problems

Three digit numbers

Three digit numbers

Time limit 1 second
Memory limit 128 MiB

Find all three digit numbers with sum of digits equals to n.

Input data

One integer n~(0 \le n \le 28).

Output data

Print in the first line the number of found three digit numbers. In the next lines print these numbers in increasing order.

Examples

Input example #1
3
Output example #1
6
102
111
120
201
210
300