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: Accepted)

#include <bits/stdc++.h>
#define int long long
#define double long double
#define endl "\n"
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define pb(x) push_back(x)
#define mp(a,b) make_pair(a,b)
#define ms(v,x) memset(v,x,sizeof(v))
#define ff first
#define ss second
#define frr(i,n) for(int i=0;i<n;i++)
#define td(v) v.begin(),v.end()
#define M   1000000007 // 1e9 + 7
#define MAXN 200100
using namespace std;
typedef pair<int,int> pii;
typedef pair<int,double> pdd;
inline int mod(int n, int m){int ret = n%m; if(ret < 0) ret += m; return ret;}
int gcd(int a, int b){return (b == 0 ? a : gcd(b, a%b));}
int exp(int a,int b,int m){
    if(b==0) return 1;
    if(b==1) return mod(a,m);
    int k = mod(exp(a,b/2,m),m);
    if(b&1){
        return mod(a*mod(k*k,m),m);
    }    else return mod(k*k,m);
}

int ok[30];

int32_t main(){
	fastio;
	int n;
	cin>>n;
	int best = 1e17;
	for(int i=1;i*i<=n;i++){
		if(n%i==0){
			best = min(best,i+n/i - 2);
		}
		
		
	}
		cout<<best<<endl;
}