Problem Statement

Takahashi loves sorting.

He has a permutation $(p_1,p_2,...,p_N)$ of the integers from $1$ through $N$. Now, he will repeat the following operation until the permutation becomes $(1,2,...,N)$:

• First, we will define high and low elements in the permutation, as follows. The $i$-th element in the permutation is high if the maximum element between the $1$-st and $i$-th elements, inclusive, is the $i$-th element itself, and otherwise the $i$-th element is low.
• Then, let $a_1,a_2,...,a_k$ be the values of the high elements, and $b_1,b_2,...,b_{N-k}$ be the values of the low elements in the current permutation, in the order they appear in it.
• Lastly, rearrange the permutation into $(b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k)$.

How many operations are necessary until the permutation is sorted?

Constraints

• $1 ≤ N ≤ 2×10^5$
• $(p_1,p_2,...,p_N)$ is a permutation of the integers from $1$ through $N$.

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print the number of operations that are necessary until the permutation is sorted.