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<iostream>
#include<algorithm>
#include<stack>
#include<queue>
#include<vector>
#include<map>
#include<math.h>
#include <iomanip>

#define rep(i, n) for(int i = 0; i < n; i++)
typedef long long ll;

using namespace std;

const int INF = 1 << 21;

int main()
{
	/*
		一回の移動回数で、i&jは1しか移動できない
		i * j 最初(1, 1)にいるから、(i - 1) + (j - 1)これが最小になるものがマスの答え
		i * j = N    i + j - 2       (√Nの計算量以下)
	*/ 

	int N;
	cin >> N;

	int loop = sqrt(N);

	int ans;
	for (int i = 1; i <= loop; i++) {
		if (N % i == 0) {
			ans = i + (N / i) - 2;
		}
	}

	cout << ans << endl;

	return 0;
}