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: Accepted)

#include<iostream>
#include<vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <functional>
using namespace std;

int main(){
	long long N;
	long long A;
	bool is = false;
	
	A = 1000000000000;

	cin >> N;

	for (long long i = sqrt(N); i >= 1; i--){
		if (N % i == 0){
			long long tmp = N / i;
			if (A > i + tmp){
				A = (i - 1) + (tmp - 1);
				is = true;
			}
		}
	}
	
	cout << A << endl;
	return 0;
}