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>
#include<stdio.h>
#include<cctype>
#include<algorithm>
#include<climits>
#include<cmath>
#include<map>
#include<vector>
#define INF INT_MAX
using namespace std;

long long N;
long long ans;
long long ans_1;
long long ans_2;
long long tmp;
long long MIN = INF;

int main(){
	cin >> N;
	ans = N - 1;
	for (int i = 1; i <= sqrt(N); i++){
		if (N%i == 0){
			ans_1 = i;
			ans_2 = N / i;
			tmp = ans_1 + ans_2 - 2;
			if (MIN > tmp){
				ans = tmp;
				MIN = ans;
			}
		}
	}

	cout << ans << endl;

	return 0;
}