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 <iostream>

using namespace std;

const size_t kMax = 1'000'000;

int main() {
  size_t N;
  cin >> N;

  size_t I = 0, J = 0;
  size_t min = 1'000'000'000'000;
  for (size_t i = N; i > 1; i--) {
    for (size_t j = 1; j < i; j++) {
      if (N == i * j && min > (i - 1) + (j - 1)) {
        min = (i - 1) + (j - 1);
        I = i;
        J = j;
      }
    }
  }
  cout << (I - 1) + (J - 1) << endl;

  return 0;
}