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 <math.h>
int main(){
  long long N,SQRT,ANS;
  scanf("%lld",&N);
  SQRT=sqrt(N);
  printf("%lld\n",N);
  while(1){
    if(N%SQRT==0){
      ANS=N/SQRT;
      printf("%lld = %lld * %lld  %lld  %lld\n",N,SQRT,ANS,SQRT*ANS,N/SQRT);
      break;
    }
    SQRT++;
  }
  printf("%lld",SQRT+ANS-2);
}