Circular Rotation Check

A carousel of numbered seats spins one step. Formally, rotate the array one position to the left: the new array b is defined by bᵢ = aᵢ₊₁ for i < n, and bₙ = a₁. The score is the number of positions that then contain their own 1-based index, i.e. positions i with bᵢ = i.

Input

The first line contains one integer n.

The second line contains n integers a₁ … aₙ.

Output

Print the score after the rotation.

Constraints

• 1 ≤ n ≤ 2·10⁴
• 1 ≤ aᵢ ≤ n

5
5 1 2 4 3

3

5
1 2 5 4 3

0