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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <math.h>
using namespace std;

long long solve(long long n){
  long long i=1, j=n;
  long long i_min=i, j_min=j;
  const long long x_limit = (long long)(ceil(sqrt(n+1)));
  
  for (long long x=2; x<=x_limit; ++x) {
    while (n%x == 0) {
      n /= x;
      i *= x;
      j /= x;
      if (i+j < i_min+j_min){
        i_min=i, j_min=j;
      }
    }
  }
  
  return (i_min-1)+(j_min-1);
}

int main(){
  long long n;
  cin >> n;
  cout << solve(n);
  return 0;
}