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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

const bool DEBUG = false;

void factorize(const long long x, vector<long long>& factors) {
  long long y = x;
  for (long long c = 2; c < y / 2 + 1; c++) {
    while (y % c == 0) {
      y /= c;
      factors.push_back(c);
    }
  }
  if (y != 1) factors.push_back(y);
}

int main(int argc, char const* argv[]) {
  long long N;
  cin >> N;

  vector<long long> factors;

  factorize(N, factors);
  reverse(factors.begin(), factors.end());
  pair<long long, long long> result{1, 1};
  for (auto&& elem : factors) {
    if (result.first < result.second) {
      result.first *= elem;
    } else {
      result.second *= elem;
    }
  }
  cout << result.first + result.second - 2 << endl;

  return 0;
}