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 <vector>
#include <stdint.h>
#include <utility>
using namespace std;
int main() {
	int64_t A;
	cin >> A;

	vector<pair<int64_t, int64_t>>v;
	for (int64_t i = 1; i*i <= A; i++) {
		if (A%i==0 ) {
			v.push_back(pair<int64_t, int64_t>(i, A / i));
		}
	}

	int64_t min=1e12;
	int64_t tmp = 0;
	for (int64_t j = 0; j < v.size(); j++) {
		tmp = v[j].first + v[j].second - 2;
		if (tmp < min) min = tmp;
	}
	cout << min << endl;
	return 0;
}