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 <iostream>
#include <string>
#include <algorithm>
#include <set>
#include <map>
#include <unordered_map>
#include <cmath>
#include <cstdio>

using namespace std;

typedef long long ll;

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) for (int i = 0; i < (n); ++i)

int main(int argc, char **argv)
{
    ll N;
    cin >> N;
    ll minCount = 1e+13;
    for (ll i = 1000001; i >= 1; --i) {
        if (N % i == 0) {
            ll j = N / i;
            ll d = (i - 1) + (j - 1);
            if (d < minCount) minCount = d;
        }
    }

    cout << minCount << endl;

    return 0;
}