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>

int main(void)
{
	int N;
	int i, j, m;

	scanf("%d", &N);

	if (2 <= N && N <= 1000000000000) {
		for (m = 1;m <= N; m++) {
			if (N < m * m) {
				for (i = 1; i <= N; i++) {
					if (N % i == 0) {
						for (j = i + 1; j <= N; j++) {
							if (N == i * j) {
								if (i + j < m + m) {
									printf("%d\n", i + j - 2);
									return 0;
								}

							}
						}

					}
				}
			}
		}
	}
	return 0;
}