#356 Permutation Flip

Statement

Statement language

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.

Sample 1

Input

5
1 2 3 4 5

Output

1

Sample 2

Input

4
2 1 4 3

Output

0