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.

Input Specification

The first line of input contains the positive integer $N$ $(2\le N\le 100000)$.

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

Output Specification

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

Sample Input 1

2
2 1

Sample Output 1

1

Sample Input 2

4
4 3 2 1

Sample Output 2

1

Sample Input 3

4
3 1 4 2

Sample Output 3

3