Permutation Flip

You are given a permutation $(A_1,A_2,\cdots,A_N)$ of $(1,2,\cdots,N)$.

You may choose two integers $l,r$ with $1 \leq l < r \leq N$ and reverse the contiguous subsequence $[A_l,A_{l+1},\cdots,A_r]$.

You must perform this operation exactly once.

Find the minimum possible number of integers $i$ ($1 \leq i \leq N$) such that $A_i=i$ after the operation.

The input is given in the following format.

$N$ $A_1\ A_2\ \cdots\ A_N$

Print the minimum possible number of integers $i$ such that $A_i=i$ after the operation.

• $2 \leq N \leq 200\ 000$.
• $1 \leq A_i \leq N$ ($1 \leq i \leq N$).
• $A_i \neq A_j$ ($1 \leq i < j \leq N$).