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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

import java.lang.Long.min

fun main (args:Array<String>){
    val N = readLine()!!.toLong()
    var minResult = (N - 1)

    for (i in 1..N) {
        for (j in i..N) {
            val result = i * j
            if (result > N) break
            if (result == N) {
                minResult = min(minResult, ((i - 1) + (j - 1)))
            }
        }
    }
    println(minResult)
}