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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main() {
  double n;
  double i;
  double sum;
  double judgesum = 0;
  int flag = 1;
  double a;
  double b;
  double ans;

  scanf ("%lf", &n);

  for (i = 2; i < 1000000; i++) {
    if (fmod(n, i) == 0 && flag == 1){
      a = n / i;
      b = i;
      sum = a + b;
      if (judgesum == sum) {
        flag = 0;
      }
    }

    judgesum = sum;
  }
  if (flag == 1) ans = n - 1;
  else ans = a + b - 2;

  printf ("%.0lf\n", ans);

  return 0;
}