SORT

문제

Consider the following sorting algorithm:

reverse-sort(sequence a)
    while (A is not in nondecreasing order)
        partition a into the minimum number of slopes
        for every slope with length greater than one
            reverse(slope)

A slope is defined as a decreasing consecutive subsequence of a. The reverse procedure will reverse the order of the elements in a slope. 

You are given a permutation of the first N natural numbers whose slopes all have even length when partitioned for the first time. Determine the total number of times reverse is called to reverse-sort the given permutation. 

입력

The first line of input contains the positive integer N (2 ≤ N ≤ 100 000). 

The second line of input contains a permutation of the first N natural numbers that needs to be sorted. 

출력

The only line of output must contain the number of times that reverse is called. 

 

2
2 1

1

4
4 3 2 1

1

4
3 1 4 2

3