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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <list>
#include <set>
#include <map>
#include <numeric>
#include <regex>
#include <tuple>
#include <iomanip>
#include <math.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> P;
#define MOD 1000000007 // 10^9 + 7
#define INF 1000000000 // 10^9
#define LLINF 1LL<<60
const double PI = 3.14159265358979323846;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	ll N; cin >> N;
	ll ans = LLINF;
	for (ll i = 1; i*i <= N; i++) {
		if (N%i == 0)ans = min(ans, i - 1LL + (N / i) - 1LL);
	}
	cout << ans << endl;

	return 0;
}