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: Time Limit Exceeded)

#include<stdio.h>

int main() {
    unsigned long x,y,z;
    unsigned long ans,tmp,ans2;
    unsigned long i = 1;
    scanf("%lu", &x);
    while (1) {
        y = x % i;
        if (y==0){
            z = x / i;
            tmp = ans;
            ans = (i + z) - 2;
            if (ans <= tmp) {
                ans2 = ans;
            }
            
        }
        if (i==x) {
            break;
        }
        
        i++;
    }
    printf("%d",ans2);
}