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 <cstdio>
#include <algorithm>
#include <cmath>
#include <iostream>
using namespace std;
long long  a, b, c, i, j, k, n, m;
int main() {
	long long  minn = 100000000;
	scanf("%lld", &a);
	for (i = 2; i <= sqrt(a)+1; i++) {
		if (a % i == 0) {
			minn = minn < (i + a / i) ? minn : (i + a / i);
		}
	}
	if (minn == 100000000)
	{
		printf("%lld", a - 1);
	}
	else
	{
		printf("%lld", minn - 2);
	}
}