Znaika has many interests. For example, now he is investigating the properties of number sets. Znaika writes down some set consisting of different positive integers (he calls this set a generating set), calculates the sum of all the written digits, and writes down the result in a special notebook. For example, for a generating set
7, 12, 43, he will write down the number 17 = 7 + 1 + 2 + 4 + 3. Znaika is sure that only magic numbers can appear as a result of this operation.
Neznaika laughs at Znaika. He thinks that there is a generating set for every number, and he even made a bet with Znaika that he would be able to construct such a set.
Help Neznaika win the bet and construct a generating set for a given number.
The only input line contains an integer n (0 < n < 105).
If it is possible to construct a generating set for the number n, output the number of elements in this set in the first line. In the second line output
a space-separated list of these elements. The elements of the set must be different positive integers strictly less than 105. If there are several generating sets, output any of them. If there are no generating sets, output −1.
Problem Author: Ivan Burmistrov
Problem Source: Ural Regional School Programming Contest 2009