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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
typedef long long ll;
int main() {
    // ifstream in("data1.txt");
    // cin.rdbuf(in.rdbuf());
    ll N;
    ll ans = 1e12;
    cin >> N;
    for(ll i = 2; i <= N; i++) {
        if(N % i == 0) {
            ll m = (i - 1) + (N / i - 1);
            if(ans == m) {
                break;
            } else {
                ans = min(ans, (i - 1) + (N / i - 1));
            }
        }
    }

    cout << ans << endl;
}