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(void){
	long N, a, b;
	scanf("%ld", &N);
	long min = sqrt(N);
	for(long i=1;i<=sqrt(N);i++){
		if(N%i==0){
			long f = i + N/i;
			if(min>f){
				min = f;
			}else if(min == f){
				a = i;
				b = N/i;
				break;
			}
		}
	}
	long ans = a-1 + b - 1;
	printf("%ld", ans);
	return 0;
}