Score : 400 points

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

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

Swapping 1 and 2 satisfies the condition.

Sample Input 3

2
2 1

Sample Output 3

The condition is already satisfied initially.

Sample Input 4

9
1 2 4 9 5 8 7 3 6