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 (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val n = readLine()?.toLong() ?: return
    fun isPrime(n: Long): Boolean {
        if (n == 2L) {
            return true
        }
        if (n % 2L == 0L) {
            return false
        }
        val last = Math.sqrt(n.toDouble()).toInt()
        var i = 3L
        while (i <= last) {
            if (n % i == 0L) {
                return false
            } else {
                i += 2L
            }
        }
        return true
    }
    if (isPrime(n)) {
        println("${n - 1}")
        return
    }
    var i = 3L
    var maxI = if (n % i == 0L) {
        i
    } else {
        1L
    }
    while (i < n) {
        i += 2
        if (isPrime(i)) {
            if (n % i == 0L) {
                maxI = i
            }
        }
    }

    println("${maxI - 1 + (n / maxI) - 1}")
}