Given a positive integer X, an X-factor chain of length m is a sequence of integers, 1 = X0, X1, X2, , Xm = X satisfying Xi < Xi+1 and Xi | Xi+1 where a | b means a perfectly divides into b. Now we are interested in the maximum length of X-factor chains and the number of chains of such length.


The input consists of several test cases. Each contains a positive integer X (X 2^20).


For each test case, output the maximum length and the number of such X-factors chains.

Sample Input

2 3 4 10 100

Sample Output

1 1 1 1 2 1 2 2 4 6


POJ Monthly--2007.10.06, ailyanlu@zsu