Dividers

All integers from $1$ to $n$ are written in a single row in some order, forming a sequence. This sequence is a permutation of the numbers $1$ through $n$.

You want to insert as many dividers into this sequence as possible. A divider can be placed between two adjacent elements of the sequence (or at the very end).

You may place a divider right after the $k$-th element only if the first $k$ elements contain every number from $1$ to $k$ exactly once. In other words, the first $k$ elements must equal the set $\{1, 2, \ldots, k\}$. In particular, a divider can always be placed right after the $n$-th element, because the whole sequence is a permutation of $1$ through $n$.

Find the maximum number of dividers you can insert.

The first line contains an integer $n$ ($1 \le n \le 10^6$), the length of the sequence.

The second line contains a permutation $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$) of the numbers $1$ through $n$, separated by spaces, where $p_i$ is the $i$-th number in the sequence.

Print a single integer: the maximum number of dividers that can be inserted.

For example, when the sequence is 2 1 3 6 5 4 9 10 8 7, the dividers can be placed as follows: 2 1 | 3 | 6 5 4 | 9 10 8 7 |. In this case there are $4$ dividers in total.