Bogosort

We have worked with sorted lists for many different problems. We have used built-in functions to sort some arrays. Yet, it’s not obvious how those built-in functions actually work under the hood. In this chapter, we’ll discuss some of the most popular sorting algorithms that are used in different places - depending on the application.

The first algorithm we’ll discuss is the most ridiculous of all of the sorting algorithms. It’s called Bogosort. It’s not used anywhere in real-world applications, and you’ll soon see why.

Given n numbers, the algorithm works by randomly shuffling those numbers and then checking if the resulting list is sorted:

from random import shuffle

a = [3, 1, -2, 5, 6]            # Initial numbers
while True:                     # Loop until the array is sorted
    is_sorted = True
    for i in range(1, len(a)):  # A loop to check if the array is sorted
        if a[i] < a[i-1]:       # If we find an element smaller then previous => it's not sorted
            is_sorted = False   # We set the variable to False and stop the loop
            break
    if is_sorted:               # If the array is sorted => stop the infinite loop
        break
    else:                       # Otherwise shuffle the list again
        shuffle(a)

print(a)                        # Finally print the resulting list

This algorithm is random and it can take infinitely long to complete. Therefore, it would be really dangerous and inefficient to use something like this in production applications.

You are asked to compute the number of iterations it would take for a Bogosort algorithm to finally find a solution.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ ).

The next line contains n space-separated integers ( ≤ ≤ ).

Output

The program should print the number of iterations it would take the Bogosort algorithm to complete the search.

Examples

Input	Output
5 5 -1 2 3 9	10

Explanation

The number 10 is a random number - it could’ve been 2, or 200. You might get different numbers when running the same program on the same input several times.

Constraints

Time limit: 30 seconds

Memory limit: 512 MB

Output limit: 1 MB