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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define rep_i(i, n) for (int i = 0; i < (n); ++i)
#define rep_ll(i, n) for (long long i = 0; i < (n); ++i)
#define r_rep_i(i, start, end) for (int i = (start); i < (end); ++i)
#define r_rep_ll(i, start, end) for (long long i = (start); i < (end); ++i)
using namespace std;

int main(){
  long long n; cin >> n;
  long long a, b;
  a = 1;
  b = 1;
  long long shortest = 100000000000000;
  r_rep_ll(i, 1, (n/2 + 1)){
    if(n % i == 0){
      b = n/i;
      shortest = min(shortest, i + b - 2);
    }
  }
    // while (a*b <= 1000000000000){
    //   if(a*b == n){
    //     shortest = a + b - 2;
    //     break;
    //   }else if(a*b > n){
    //     break;
    //   }
    //   b += 1;
    // }
  cout << shortest << endl;
}