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.