Description

Sudden rain at the apartment leaves some residents without umbrellas. Residents with spare umbrellas can only lend to immediately adjacent units. Find the maximum number of residents who can commute.

Input

Output

Constraints

• •2 <= n <= 30
• •1 <= lost length <= n
• •1 <= reserve length <= n
• •Residents with spare umbrellas might also be without one (use their own)

Examples

n = 7, lost = [2, 3, 5, 7], reserve = [1, 3, 4, 6]

7