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++ (GCC 9.2.1) (judge verdict: Accepted)

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

bool is_Prime(long long N){
  if(N == 1)return false;
  for(long long i = 2; i*i <=N; i++){
    if(N %  i== 0)return false;
  }
  return true;
}

int main(){
  long long N;
  cin >> N;
  if(is_Prime(N)){
    cout << N - 1 << endl;
    return 0;
  }
  long long ans = 0;
  
  for(long long i = 1; i*i <=N; i++){
    if(N % i == 0){//割り切れるとき
      long long a = i;
      long long b = N / a;
      ans = a + b -2; //1,1スタートなので(下に1,右に1移動してからスタート)2を引く
    }
  }
  cout << ans << endl;
}