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: Accepted)

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

unsigned long Sqrt(unsigned long x) {
    unsigned long i=1;
    while(1) {
        if(i*i > x) {
            break;
        }
        i++;
    }
    if(i-1 > 1) {
        return i-1;
    }
    return 1;
}


int main() {
    unsigned long N;
    scanf("%lu", &N);
    unsigned long m = Sqrt(N);

    unsigned long i;
    unsigned long j;
    i = m;
    while(1) {
        if(N % i == 0) {
            break;
        }
        i--;
    }
    j = N / i ;
    unsigned long mini = i + j;
    printf("%lu\n", mini-2);
    return 0;
}