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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Windows;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

class Program
{
    static void Main(string[] args)
    {
      //入力を受け取る
      var N = long.Parse(Console.ReadLine());
      long i = 1;
      long j = 1;
      long sqrt = (long) Math.Floor(Math.Sqrt(N));
      long min = long.MaxValue;
      
      if(Factorization(N).Count() != 1){
        for(int a = 1 ; a <= sqrt ; a++){
          for(int b = a ; b <= sqrt ; b++){
            if(a*b == N && min > a+b -2){
              min = a+b -2;
            }
          }
        }
      }else{
        min = N -1;
      }
      Console.WriteLine(min);
    }
  
  static Dictionary<long,long> Factorization(long n){
    var sqrt = Math.Floor(Math.Sqrt(n));
    var result = new Dictionary<long,long>();
    
    for(long i = 2; i < sqrt ; i++){
      if(n%i == 0){
        var r = 0;
        while(n%i == 0){
          r++;
          n = n/i;
        }
        result.Add(i,r);
      }
    }
    if(n > sqrt){
      result.Add(n,1);
    }
    return result;
  }

}