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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main (input){
  input = input.split("\n");
  tmp = input[0].split(" ");
  var N = parseInt(tmp[0],10);
  var x = 0;
  var y = 0;
  if(N<1){"";
  }else{
    for(x=2;x<N;x++){
      if(N % x == 0){
        console.log(x);
        y=N-x;
      }else{"";}
    }
  }
  console.log(x+y-2);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));