Necklace of Beads

http://poj.org/problem?id=1286

// File Name: poj1286.cpp
// Author: bo_jwolf
// Created Time: 2013年10月07日 星期一 21:31:08

#include<vector>
#include<list>
#include<map>
#include<set>
#include<deque>
#include<stack>
#include<bitset>
#include<algorithm>
#include<functional>
#include<numeric>
#include<utility>
#include<sstream>
#include<iostream>
#include<iomanip>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<ctime>

#define INT long long int

using namespace std;
INT gcd( INT a, INT b){
	return b == 0? a: gcd( b, a % b );
}

INT c = 3, s;
INT polya(){
	INT ans = 0;
	for( INT i = 0; i < s; ++i ){
		ans += (INT)pow( 1.0 * c, gcd( s, i ) );
	}
	if( s % 2 ){
		ans += s * ( INT )pow( 1.0 * c, ( s / 2 + 1 ) );
	}
	else{
		ans += s / 2 * ( INT )pow( 1.0 * c, s / 2 );
		ans += s / 2 * ( INT )pow( 1.0 * c, s / 2 + 1 );
	}
	return ans / 2 / s;
}

int main(){
	INT ans;
	while( scanf( "%lld", &s ) != EOF ){
			if( s == -1 )
				break;
			if( s == 0 )
				ans = 0;
			else
				ans = polya();
			printf( "%lld\n", ans );
	}
return 0;
}