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 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>
#include <stdlib.h>

int main(){
  long int n, ans[2], i;
  i = scanf("%ld", &n);
  if(n == 2 || n == 3){printf("%ld\n", n - 1);exit(0);}
  for(i = (long int)sqrt((double)n) - 1; i < n; i++){
    if(n % i == 0){
      ans[0] = i;
      ans[1] = n / i;
      break;
    }
  }
  printf("%ld\n", ans[0] + ans[1] - 2);
}