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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<string.h>
#include<stdio.h>

using namespace std;
int main() {
	long long a;
	long long b;

	cin >> a;
	cout << a << endl;
	long long i = 0;
	long long k = 1;
	int t = 0;
	for (i = 1; i <= a / 2; i++) {
		if (a % i == 0) {
			if (abs(a / i - i) < abs(a / k - k)) {
				k = i;
			}
		}

	}
	int ans = (k - 1) + (a / k - 1);


	


	cout << ans << endl;

}