AT_abc420_g [ABC420G] sqrt(n²+n+X)

You are given an integer $ X $ . Find all integers $ n $ such that $ \displaystyle \sqrt{n^2+n+X} $ is an integer.

The input is given from Standard Input in the following format: > $ X $

Let $ N_1,N_2,\ldots,N_K $ be the integers $ n $ such that $ \displaystyle \sqrt{n^2+n+X} $ is an integer, listed in ascending order (where $ K $ is the number of $ n $ satisfying the condition). Output in the following format: > $ K $ $ N_1 $ $ N_2 $ $ \ldots $ $ N_K $

### Sample Explanation 1 There are four integers $ n $ such that $ \sqrt{n^2+n+4} $ is an integer: $ n=-4,-1,0,3 $ . ### Constraints - $ -10^{14} \le X\le 10^{14} $ - The input value is an integer.