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 <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

using ll = long long; using ld = long double; using vll = vector<ll>; using vvll = vector<vll>; using vld = vector<ld>; 
using vi = vector<int>; using vvi = vector<vi>;
using P = pair<ll, ll>;

template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) {  o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args> 
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; cout << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]";  return o; }
template <typename T>  ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]";  return o; }
template <typename T, typename U>  ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]";  return o; }
#define VN(v) # v
#define print(a) cout << a << "#" << VN(a) << endl;

static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;

int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    ld d; cin >> d;
    ld ret = d*sqrtl(2.0l);
    if (d < sqrtl(floorl(d)*floorl(d)+1.0l)) {
        chmax(ret, floorl(d)+1.0l);
    }
    cout << setprecision(40) << ret << endl;
    
    return 0;
}