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>
#define ll long long int

ll a[2] = {1, 1};

int findFactors(ll num){
    int i;
    while (num % 2 == 0){ // 偶数の素数は2のみ
        if(a[0] <= a[1]) {
            a[0] *= 2;
        } else {
            a[1] *= 2;
        }
        num /= 2;
    }
    for (i = 3; i <= num/2+1; i++){ // 他の素数で割っていく
        while (num % i == 0){
            if(a[0] <= a[1]) {
                a[0] *= i;
            } else {
                a[1] *= i;
            }
            num /= i;
        }
    }
    if(a[0] <= a[1]) {
        a[0] *= num;
    } else {
        a[1] *= num;
    }
    return 0;
}
int main(void) {
    ll n;
    scanf("%lld", &n);
    findFactors(n);
    printf("%lld\n", a[0]+a[1]-2);
    return 0;
}