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;
      
       foreach(KeyValuePair<long,long> item in Factorization(N)){
          //Console.WriteLine("[{0}:{1}]", item.Key, item.Value);
         if(item.Value%2 == 0){
           i *=  (item.Value/2)*item.Key;
           j *=  (item.Value/2)*item.Key;
         }else{
           if(i < j){
             if(item.Value/2 != 0){
               j *=  (item.Value/2)*item.Key;
             }
             i *=  (item.Value/2+1)*item.Key;
           }else{
             if(item.Value/2 != 0){
               i *=  (item.Value/2)*item.Key;
             }
             j *=  (item.Value/2+1)*item.Key;
           }
         }
       }
      Console.WriteLine(i+j-2);
    }
  
  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;
  }

}