GF2 - Irreducible polynomials over GF2

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Find the number of degree n irreducible polynomials over GF(2). For example: for n=1 there are two such polynoms: x and x+1. For n=2 there is only one: x2+x+1. Note that in R[x] the polynom x2 +1 is irreducible, but not over GF(2), because x2+1=(x+1)*(x+1)

Input

A single positive integer n, where n<500000

Output

Output the answer for n.

Example

Input:
201
Output:
15989433276208858463104100421305100522608250813995004946218

Input:
1
Output:
2

Input:
2
Output:
1

Input:
3
Output:
2


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[Trichromatic] XilinX: 2009-05-26 08:31:50

I've solved this problem in MIPT Online Judge by Ruby, but it seems that Ruby works pretty slow in SPOJ.

Last edit: 2009-05-26 02:21:16
Robert Gerbicz: 2009-05-26 08:31:50

Java and Python are too slow on this problem. You can try c/c++ or haskell.


Added by:Robert Gerbicz
Date:2009-05-25
Time limit:0.100s-1s
Source limit:4096B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO
Resource:classic problem, own input