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)

const main = (N) => {
    var r = N
    const end = Math.ceil(Math.sqrt(N))+1
    for(var i =1;i<end;i++) {
        if(N % i == 0) {
            const k = Math.ceil(N/i)
            if(r > Math.abs(k-i)) {
                r = i+k
            }
        }
    }
    return r
}
const input = require('fs').readFileSync("/dev/stdin","utf8").split("\n")[0]
const N = Number(input)
console.log(main(N)-2)