记录编号	160579	评测结果	AAAAAAAAAA
题目名称	[HAOI 2015]按位或	最终得分	100
用户昵称	Asm.Def	是否通过	通过
代码语言	C++	运行时间	1.778 s
提交时间	2015-04-28 20:24:38	内存使用	8.29 MiB

/***********************************************************************/
/**********************By Asm.Def-Wu Jiaxin*****************************/
/***********************************************************************/
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cctype>
#include <algorithm>
using namespace std;
#define SetFile(x) ( freopen(#x".in", "r", stdin), freopen(#x".out", "w", stdout) );
//#define UseFREAD
#ifdef UseFREAD
#define getc() *(file_ptr++)
#define FreadLenth 5000000
char CHARPOOL[FreadLenth], *file_ptr = CHARPOOL;
#else
#define getc() getchar() 
#endif
#ifdef DEBUG
#include <sys/timeb.h>
timeb SysTp;
#endif
template<class T>inline void getd(T &x){
	char ch = getc();bool neg = false;
	while(!isdigit(ch) && ch != '-')ch = getc();
	if(ch == '-')ch = getc(), neg = true;
	x = ch - '0';
	while(isdigit(ch = getc()))x = x * 10 - '0' + ch;
	if(neg)x = -x;
}
/***********************************************************************/
const int maxn = 1 << 20;
const double eps = 1e-8;
double P[maxn];
int n, N;
inline double m_abs(double x) {return x < 0 ? -x : x;}
inline void work(){
	getd(n);N = 1 << n;
	int i, j, t, tmp;

	for(i = 0;i < N;++i){
		scanf("%lf", P + i);
		if(P[i])tmp |= i;
	}
	if(tmp+1 != N){
		puts("INF");
		return;
	}

	for(t = 1;t < N;t <<= 1)//Modulate
		for(j = 0;j < N;++j)if(j & t)P[j] += P[j ^ t];

	for(j = 0;j < N;++j){
		if(m_abs(P[j] - 1.0) < eps)P[j] = 0;
		else P[j] = 1.0 / (P[j] - 1.0);
	}

	for(t = 1;t < N;t <<= 1)//Demodulate
		for(j = 0;j < N;++j)if(j & t)P[j] -= P[j ^ t];

	printf("%.10lf\n", P[N - 1]);
}

int main(){

#ifdef DEBUG
	freopen("test.txt", "r", stdin);ftime(&SysTp);
	size_t Begin_sec = SysTp.time, Begin_mill = SysTp.millitm;
#elif !defined ONLINE_JUDGE
	SetFile(haoi2015_set);
#endif

#ifdef UseFREAD
	fread(file_ptr, 1, FreadLenth, stdin);
#endif

	work();

#ifdef DEBUG
	ftime(&SysTp);
	printf("\n%.3lf sec \n", (SysTp.time - Begin_sec) + (SysTp.millitm - Begin_mill) / 1000.0);
#endif
	return 0;
}