Problem:
Score : 300 points

Problem Statement

Takahashi is standing on a multiplication table with infinitely many rows and columns.

The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).

In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).

Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.

Sample Input 2

50

Sample Output 2

13

(5, 10) can be reached in 13 moves.

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#include <numeric>
#include <queue>
#include <sstream>
#include <unordered_map>
#include <cstring>
#include <iomanip>

using namespace std;

typedef long long ll;

const ll INF=1e9+7;

template<class T> inline bool chmin(T& a, T b) {if (a > b) {a = b;return true;}return false;}
template<class T> inline bool chmax(T& a, T b) {if (a < b) {a = b;return true;}return false;}

#define rep(i,n) for(int i=0;i<(n);i++)

int main(){
    ll N,min=INF,x,y;
    cin>>N;
    for(ll i=2;i<=floor(sqrt(N));i++){
        if(N%i==0){
            ll a=N/i;
            ll b=i;
            if(min>abs(a-b)){
                x=a-1;
                y=b-1;
                min=abs(a-b);
            }
        }
    }
    if(min==INF){
        cout<<N-1<<endl;
        return 0;
    }
    cout<<x+y<<endl;
    return 0;
}

//a=97,z=122

//6,15の時