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: Time Limit Exceeded)

#include<stdio.h>

void takahashi(long long int N){
	long long int i, a, b, c, min;
	min = N;
	for(i = 1; i <= N/2; i++){
		if(N%i == 0){
			a = i - 1;
			b = (N / i) -1;
			c = a + b;
			if(c <= min){
				min = c;
			}
		}
	}
	printf("%lld\n", min);
}

int main(){
	long long int N;
	scanf("%lld", &N);
	takahashi(N);
	return 0;
}