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>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
typedef long long ll;
long long MOD = 1e9 + 7;
using namespace std;

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

  vector<ll> ya;

  ll ku = 0;
  if (N % 2 == 0) {
    ku = N / 2;
  } else {
    ku = (N + 1) / 2;
  }
  for (ll i = 1; i < ku + 1; i++) {
    if (N % i == 0) {
      ya.push_back(i);
    }
  }

  ll res = 1e12 + 1;

  for (const ll &e : ya) {
    res = min(res, e + (N / e) - 2);
  }
  cout << res << endl;
  return 0;
}