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 <iostream>

using namespace std;

int main(){
    long long int N;
    cin >> N;
    //long long int times;
    long long int a,b;
    a = 1;
    b = 1;
    bool prime=true;
    while (N % 2 == 0)
    { // 偶数の素数は2のみ
        a *= 2;
        N /= 2;
        prime = false;
    }
    for (int i = 3; i*i <= N; i=i+2)
    { // 他の素数で割っていく
        while (N % i == 0)
        {
            a *= i;
            N /= i;
            b = i;
            prime = false;
        }
    }
    if(prime) cout << N-1 << endl;
    else {
        a /= b;
        cout << (a-1)+ (b-1) << endl;
    }
    return 0;
}