There are 8 prison cells in a row, and each cell is either occupied or vacant.
Each day, whether the cell is occupied or vacant changes according to the following rules:
If a cell has two adjacent neighbors that are both occupied or both vacant, then the cell becomes occupied.
Otherwise, it becomes vacant.
(Note that because the prison is a row, the first and the last cells in the row can't have two adjacent neighbors.)
We describe the current state of the prison in the following way: cells[i] == 1 if the i-th cell is occupied, else cells[i] == 0.
Given the initial state of the prison, return the state of the prison after N days (and N such changes described above.)
Example 1:
Input: cells = [0,1,0,1,1,0,0,1], N = 7
Output: [0,0,1,1,0,0,0,0]
Explanation: 
The following table summarizes the state of the prison on each day:
Day 0: [0, 1, 0, 1, 1, 0, 0, 1]
Day 1: [0, 1, 1, 0, 0, 0, 0, 0]
Day 2: [0, 0, 0, 0, 1, 1, 1, 0]
Day 3: [0, 1, 1, 0, 0, 1, 0, 0]
Day 4: [0, 0, 0, 0, 0, 1, 0, 0]
Day 5: [0, 1, 1, 1, 0, 1, 0, 0]
Day 6: [0, 0, 1, 0, 1, 1, 0, 0]
Day 7: [0, 0, 1, 1, 0, 0, 0, 0]
Example 2:
Input: cells = [1,0,0,1,0,0,1,0], N = 1000000000
Output: [0,0,1,1,1,1,1,0]
Note:
cells.length == 8
cells[i] is in {0, 1}
1 <= N <= 10^9
class Solution:
    def prisonAfterNDays(self, cells: List[int], N: int) -> List[int]:
        visited = {str(cells) : N}
        
        cycle = 0
        hascycle = False
        
        def get_next(cells) -> List[int]:
            '''return next cell'''
            tmp = [0] + [cells[i-1] ^ cells[i+1] ^ 1 for i in range(1,7)] + [0]
            return tmp
            
        
        while N > 0:
            visited[str(cells)] = N
            
            N -= 1
            cells = get_next(cells.copy())
            if str(cells) in visited:
                hascycle = True
                cycle = visited[str(cells)] - N 
                break
            
            
        if hascycle:
            N = N % cycle
            while N > 0:
                N -= 1
                cells = get_next(cells)
            
        return cells
class Solution:
    def prisonAfterNDays(self, cells: List[int], N: int) -> List[int]:
        visited = {str(cells) : N}
        
        cycle = 0
        hascycle = False
        
        def get_next(cells) -> List[int]:
            '''return next cell'''
            tmp = [0] + [cells[i-1] ^ cells[i+1] ^ 1 for i in range(1,7)] + [0]
            return tmp
            
        
        while N > 0:
            visited[str(cells)] = N
            
            N -= 1
            cells = get_next(cells.copy())
            if str(cells) in visited:
                hascycle = True
                cycle = visited[str(cells)] - N 
                break
            
            
        if hascycle:
            N = N % cycle
            while N > 0:
                N -= 1
                cells = get_next(cells)
            
        return cells