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>
typedef long long int lli;
lli gcd(lli a,lli b);
int main(void)
{
    lli N;
    scanf("%lld", &N);
    lli min = N;
    lli tmp;
    for (lli i = 1; N%i==0; i++)
    {
        if (gcd(N, i) == i)
        {
          lli j = N/i;
            tmp = (i - 1) + (j - 1);
            if(tmp<min){
                min = tmp;
            }
        }
    }
  printf("%lld",min);
    return 0;
}

lli gcd(lli a, lli b)
{
    lli tmp;
    lli r;
    if (a < b)
    {
        tmp = a;
        a = b;
        b = tmp;
    }
    r = a % b;
    while (r != 0)
    {
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}