1. Question 1

You are given the first 2^N integers, of which K are "special".
Your task is to remove all the integers from the array with the minimum possible cost, following these rules:

Removal Rules

1.

If a segment contains L integers, and X of them are special, the cost of removing this segment is calculated as:
Cost = L × X × P, where P is a constant.

2.

If a segment contains L integers, and none are special, the cost of removing this segment is:
Cost = Q, where Q is another constant.

3.

If a segment contains L integers and L is divisible by 2, you have two options:
Option 1: Use either of the rules above to remove the segment as is
Option 2: Divide the segment into two smaller segments, each containing L/2 integers, and
recursively find the removal cost for both parts separately, then add the costs together.

Find the minimum cost of removing all 2^N integers, modulo (10^9 + 7).

NOTE: The integers must remain in their original order while dividing the current part into two smaller parts. If the current part contains integers [1, 2, 3, 4], the only correct way to divide it is [1, 2] and [3, 4].

Example

N = 2
P = 2
Q = 1
special_integers = [1, 3]

Start with the first 2^N integers: [1, 2, 3, 4] in which integers 1 and 3 are special, shown in bold.

2. Question 2

A permutation P is called unstable if it keeps changing every second based on the rule below.

• Every element of the permutation is changing every second independently following a rule, i.e., after one second every P[i] becomes P[P[i]]

Given a permutation, find the minimum time after which it will become stable. If it will never become stable, return -1.

Example

Given N = 3 and P = [3,2,1],
In one second it will become P[P[3]], P[P[2]], P[P[1]] = [1, 2, 3].
The permutation [1,2,3] is stable as it will not change further after applying the same rule again.

Function Description

Complete the function solve in the editor below. The function should return a single integer as stated above.

solve has the following parameter:

• P[1]...P[n]: an array of integers

Constraints

• 1 ≤ n ≤ 10⁵
• 1 ≤ P[i] ≤ n

Input Format For Custom Testing

The first line contains an integer n that denotes the length of permutation.
The second line contains permutation P of n distinct space-separated integers.

Sample Case 0

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