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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <numeric>
#include <map>

using namespace std;

typedef long long ll;

map< ll, ll > prime_factor(ll n) {
    map< ll, ll > ret;
    for(ll i = 2; i * i <= n; i++) {
        while(n % i == 0) {
            ret[i]++;
            n /= i;
        }
    }
    if(n != 1) ret[n] = 1;
    return ret;
}

int main(void)
{
    ll ans = 0;
    ll n;
    ll count = 0;
    ll sum = 0;
    
    cin >> n;
    
    map< ll, ll > a = prime_factor(n);
    
    for(auto p : a) {
        count += p.second;
    }
    
    for(auto p : a) {
        while (count-- > 0 && p.second--) {
            if (sum == 0) {
                sum = p.first;
            } else {
                sum *= p.first;
            }
        }
    }
    ans = sum + (n / sum) - 2;
    
    cout << ans << endl;
    return 0;
}