Nayeon Sort

Nayeon, who studied hard in her data structures class, devised a new sorting algorithm and named it Nayeon sort after herself. Given an array $A=[a_1,a_2,\cdots,a_N]$ to sort, Nayeon sort works as follows.

1. Declare as many empty stacks as you want.
2. Insert each element from $a_1$ to $a_N$, in order, into any stack you choose.
3. Declare an empty array $B$.
4. Repeat until every stack is empty: pop one element from any stack you choose and append it to the end of $B$.

Whether Nayeon sort can sort the array depends on the array and on how many stacks you use. For example, if $A=[9,2,8,7,1]$, put $[9,8]$, $[2]$, and $[7,1]$ into three stacks, then pop from the third, second, third, first, and first stacks in that order. The result is the array sorted in ascending order. Two stacks are enough to sort $A$, but with only one stack, $A$ cannot be sorted in ascending order.

Nayeon offers to secretly add one problem to your HCPC solve count if you find the minimum number of stacks needed to sort the given array in ascending order. Solve it before anyone else and get one step closer to winning HCPC!

The first line contains the length $N$ of the array $A$. ($1 \le N \le 500,000$)

The second line contains $N$ integers $a_1, a_2, \cdots, a_N$, separated by spaces. ($1 \le a_i \le 10^9$)

On the first line, print the minimum number of stacks needed to sort $A$ in ascending order.