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>
using namespace std;
using ll = long long;

#define REP(i,n) for(ll i=0; i < (n); ++i)
#define REPR(i,n) for(ll i=(n); i >= 0; --i)
#define FOR(i, m, n) for(ll i = (m); i < (n); ++i)

#define INF 1e12+5

int main(){
  ll N;
  cin >> N;
  ll ans = INF;
  FOR(i, 1, ll(sqrt(N)+1)){
    if(N % i == 0){
      ll x = i, y = N/i;
      //cout << x << " " << y << endl;
      ans = min(ans, x-1+y-1);
    }
  }
  cout << ans << endl;
  return 0;
}