#SEQ6. Consecutive sequence

Consecutive sequence

We define consecutive sequence as a sequence of integer numbers {n, n+1, n+2, ..., n+m}. For each given positive integer N ≤ 107 calculate number of such sequences which sum is equal to N.

Input

The input file consists of multiple lines (about 103 in the first data set and 105 in the second), each line contains integer N. The input is terminated with N = 0, which should not be processed.

Output

Expected number in each line

Example

Input:

500
0

Output:

8