Problem: In Manhattan, roads run where the x or y coordinate is an integer. Both Sunuke-kun's house and Sumeke-kun's house are on the road, and the straight line distance (Euclidean distance) is just d. Find the maximum value that can be considered as the shortest distance when traveling along the road from Sunuke-kun's house to Sumek-kun's house.

Constraints

* 0 <d ≤ 10
* d is given up to exactly three decimal places

Input


d


Output

Print the answer on one line. If the absolute error or relative error is 10-9 or less, the answer is judged to be correct.

Examples

Input

1.000


Output

2.000000000000


Input

2.345


Output

3.316330803765

Solution (in CPP):

Solution:
#include <iostream>
#include <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <tuple>
#include <queue>
#include <set>
#include <cstdio>
#include <climits>
#include <cmath>
#include <array>
#include <functional>
#include <list>
#include <iomanip>
#include <set>
const int MOD=1000000007;
const int INF=1000000000;
using namespace std;
typedef long long ll;
typedef vector<int> vi;
const double eps=1e-9;
const int inf=1e9;
typedef pair<int,int> P;
struct Point
{
  double x,y;
  Point(){x=0;y=0;}
  Point(double d_x,double d_y){x=d_x,y=d_y;}
  double operator*(Point obj){return obj.x*x+obj.y*y;}
  double operator%(Point obj){return obj.y*x-obj.x*y;}
  Point operator*(double b){Point tmp;tmp.x=x*b;tmp.y=y*b;return tmp;}
  Point operator/(double b){Point tmp;tmp.x=x/b;tmp.y=y/b;return tmp;}
  Point operator+(Point obj){Point tmp;tmp.x=x+obj.x;tmp.y=y+obj.y;return tmp;}
  Point operator-(){Point tmp;tmp.x=-x;tmp.y=-y;return tmp;}
  Point operator-(Point obj){Point tmp;tmp.x=x-obj.x;tmp.y=y-obj.y;return tmp;}
  Point operator-=(Point obj){x-=obj.x;y-=obj.y;return *this;}
  Point operator+=(Point obj){x+=obj.x;y+=obj.y;return *this;}
  Point operator/=(double b){x=x/b;y=y/b;return *this;}
  Point operator*=(double b){x=x*b;y=y*b;return *this;}
  double size(){return hypot(x,y);}
  Point unit(){return Point(x/size(),y/size());}
  Point normal(){return Point(y,-x);}
  double atan(){return atan2(y,x);}
};

bool operator<(Point a,Point b){return a.x!=b.x?a.x<b.x:a.y<b.y;}
bool operator>(Point a,Point b){return b<a;}
bool operator<=(Point a,Point b){return !(b<a);}
bool operator>=(Point a,Point b){return !(a<b);}
bool operator==(Point a,Point b){return (a-b).size()<eps;}
bool operator!=(Point a,Point b){return !(a==b);}

bool equal(double a,double b){return abs(a-b)<eps;}
double cross(Point a,Point b){return a%b;}
double dot(Point a,Point b){return a*b;}

int ccw(Point a,Point b,Point c)
{
  b=b-a;
  c=c-a;
  if(b%c>0) return +1;
  else if(b%c<0)return -1;
  else if(b*c<0) return +2;
  else if(b.size()<c.size()) return -2;
  else return 0;
}

double d;
int main(int argc,char const* argv[])
{
  cin >> d;
  double ans=d*sqrt(2);
  for(int x=1;x<=10;x++)
    {
      if(d*d-x*x>=0)
	{
	  double y=sqrt(max(0.0,d*d-x*x));
	  ans=max(ans,x+(y<1.0 ? 1.0 : y) );
	}
    }
  cout << fixed << setprecision(12) << ans << endl;
  return 0;
}