You are given integer positive number N. Find the number of solutions in positive integer numbers of the following equation:

Input

Each line of input file contains one integer number N (1 ≤ N ≤ 10⁴). The last line contains 0 and shouldn't be processed. Number of lines in the input does not exceed 30.

Output

For every line in the input write the answer on a separate line.

Example

Input:
1
2
0

Output:
1
3