200821: [AtCoder]ARC082 D - Derangement

Problem Statement

You are given a permutation $p_1,p_2,...,p_N$ consisting of $1$,$2$,..,$N$. You can perform the following operation any number of times (possibly zero):

Operation: Swap two adjacent elements in the permutation.

You want to have $p_i ≠ i$ for all $1≤i≤N$. Find the minimum required number of operations to achieve this.

Constraints

• $2≤N≤10^5$
• $p_1,p_2,..,p_N$ is a permutation of $1,2,..,N$.

Input

The input is given from Standard Input in the following format:

$N$
$p_1$ $p_2$ .. $p_N$

Output

Print the minimum required number of operations

Sample Input 1

5
1 4 3 5 2

Sample Output 1

2

Swap $1$ and $4$, then swap $1$ and $3$. $p$ is now $4,3,1,5,2$ and satisfies the condition. This is the minimum possible number, so the answer is $2$.

Sample Input 2

2
1 2

Sample Output 2

1

Swapping $1$ and $2$ satisfies the condition.

Sample Input 3

2
2 1

Sample Output 3

0

The condition is already satisfied initially.

Sample Input 4

9
1 2 4 9 5 8 7 3 6

Sample Output 4

3