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;
using ll = long long;
using vi = vector<int>;
using vs = vector<string>;
using vvi = vector<vi>;
using vvs = vector<vs>;
using pli = pair<long long, int>;
using vpli = vector<pli>;

int main() {
  ll N, Nsq, d_final = 10000000000000;
  cin >> N;
  Nsq = sqrt(N);
  cerr << Nsq << endl;
  
  if (Nsq < 2) {
    cout << N - 1 << endl;
  }
  else {
    for (int i = 1; i < Nsq + 1 ; i++) {
      ll Ntmp = N;
      if (N % i == 0) {
        d_final = min(d_final, i + N / i);
      }
    }
    cout << d_final - 2 << endl;
  }
  
}