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 <stdio.h>
#include <math.h>

int main() {
	long long int N, e[10000000] = { 0 }, t = 1, x, y;
	scanf("%lld", &N);
	for (int i = 1; i <= 1000000; i++) {
		if (N % i == 0) {
			e[t] = i;
			t++;
		}
	}
	int r = 1;
	long double ne = (long double)N;
	long long int n = (long long int)sqrt(ne);
	while (e[r] < n) {
		r++;
	}
	x = e[r];
	y = N / x;
	printf("%lld", x + y - 2);
	return 0;
}