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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define REP2(i, a, b) for (int i = (a); i < (int)(b); i++)
#define RREP2(i, a, b) for (int i = (a); i > (int)(b); i--)
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef long long ll;

ll Main(ll &n)
{
    ll sq = sqrt(n);
    ll a = 0;
    ll b = 0;
    for (ll i = sq; i > 0; i--)
    {
        if(n % i == 0)
        {
            a = n / i;
            break;
        }
    }
    b = n / a;
    return a + b - 2;
}

int main(void){
    ll N;
    cin >> N;
    cout << Main(N) << endl;
    return 0;
}