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 calc144C(N:Int): Int {
    fun factorize(n0:Long):List<Pair<Long,Int>>{
        val res = mutableListOf<Pair<Long, Int>>()
        var i = 2L
        var n = n0
        while (i * i <= n) {
            if (n % i != 0L){
                i++
                continue
            }
            var c = 0
            while ( n % i == 0L){
                n /= i
                c++
            }
            res.add(i to c)
            i ++
        }
        if (n != 1L){
            res.add(n to 1)
        }
        return res
    }

    val factors = factorize(N.toLong())
    return factors.fold(0){ acc, pair -> acc + pair.second}
}

fun main(args: Array<String>) {
    val (N) = readLine()!!.map { it.toInt() }
    println(calc144C(N))
}