You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given two integer arrays energyDrinkA and energyDrinkB of the same length n by a futuristic sports scientist. These arrays represent the energy boosts per hour provided by two different energy drinks, A and B, respectively.
You want to maximize your total energy boost by drinking one energy drink per hour. However, if you want to switch from consuming one energy drink to the other, you need to wait for one hour to cleanse your system (meaning you won't get any energy boost in that hour).
Return the maximum total energy boost you can gain in the next n hours.
Note that you can start consuming either of the two energy drinks.

Example 1:

Input: energyDrinkA = [1,3,1], energyDrinkB = [3,1,1]
Output: 5
Explanation:
To gain an energy boost of 5, drink only the energy drink A (or only B).

Example 2:

Input: energyDrinkA = [4,1,1], energyDrinkB = [1,1,3]
Output: 7
Explanation:
To gain an energy boost of 7:

Drink the energy drink A for the first hour.
Switch to the energy drink B and we lose the energy boost of the second hour.
Gain the energy boost of the drink B in the third hour.

Constraints:

n == energyDrinkA.length == energyDrinkB.length
3 <= n <= 105
1 <= energyDrinkA[i], energyDrinkB[i] <= 105

Your solution to the problem should be a method of the class Solution called maxEnergyBoost and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxEnergyBoost(self, energyDrinkA: List[int], energyDrinkB: List[int]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given two integer arrays energyDrinkA and energyDrinkB of the same length n by a futuristic sports scientist. These arrays represent the energy boosts per hour provided by two different energy drinks, A and B, respectively.
You want to maximize your total energy boost by drinking one energy drink per hour. However, if you want to switch from consuming one energy drink to the other, you need to wait for one hour to cleanse your system (meaning you won't get any energy boost in that hour).
Return the maximum total energy boost you can gain in the next n hours.
Note that you can start consuming either of the two energy drinks.

Example 1:

Input: energyDrinkA = [1,3,1], energyDrinkB = [3,1,1]
Output: 5
Explanation:
To gain an energy boost of 5, drink only the energy drink A (or only B).

Example 2:

Input: energyDrinkA = [4,1,1], energyDrinkB = [1,1,3]
Output: 7
Explanation:
To gain an energy boost of 7:

Drink the energy drink A for the first hour.
Switch to the energy drink B and we lose the energy boost of the second hour.
Gain the energy boost of the drink B in the third hour.

Constraints:

n == energyDrinkA.length == energyDrinkB.length
3 <= n <= 105
1 <= energyDrinkA[i], energyDrinkB[i] <= 105

Your solution to the problem should be a method of the class Solution called maxEnergyBoost and should pass all tests. Use the following starter code:
```python
class Solution:
    def maxEnergyBoost(self, energyDrinkA: List[int], energyDrinkB: List[int]) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().maxEnergyBoost(energyDrinkA = [1,1,1,1,1,1], energyDrinkB = [1,1,1,1,1,1]) == 6

assert Solution().maxEnergyBoost(energyDrinkA = [1,100000,1], energyDrinkB = [100000,1,100000]) == 200001

assert Solution().maxEnergyBoost(energyDrinkA = [4,1,1], energyDrinkB = [1,1,3]) == 7

assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5,5], energyDrinkB = [1,1,1,1]) == 20

assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5], energyDrinkB = [5,5,5]) == 15

assert Solution().maxEnergyBoost(energyDrinkA = [10,20,30], energyDrinkB = [30,20,10]) == 60

assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5,5], energyDrinkB = [5,5,5,5]) == 20

assert Solution().maxEnergyBoost(energyDrinkA = [100000,100000,100000], energyDrinkB = [1,1,1]) == 300000

assert Solution().maxEnergyBoost(energyDrinkA = [5,6,7], energyDrinkB = [3,2,1]) == 18

assert Solution().maxEnergyBoost(energyDrinkA = [1,2,3,4,5], energyDrinkB = [5,4,3,2,1]) == 18

assert Solution().maxEnergyBoost(energyDrinkA = [1,3,1], energyDrinkB = [3,1,1]) == 5

assert Solution().maxEnergyBoost(energyDrinkA = [3,2,5,10,7], energyDrinkB = [8,4,1,9,6]) == 30

assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5], energyDrinkB = [10, 10, 10, 10, 10]) == 50

assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 5, 7, 9], energyDrinkB = [2, 4, 6, 8, 10]) == 30

assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5], energyDrinkB = [1, 2, 3, 4, 5]) == 25

assert Solution().maxEnergyBoost(energyDrinkA = [10,20,30,40,50], energyDrinkB = [50,40,30,20,10]) == 180

assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 2, 4, 5, 6], energyDrinkB = [6, 5, 4, 3, 2, 1]) == 26

assert Solution().maxEnergyBoost(energyDrinkA = [10, 1, 1, 1, 10], energyDrinkB = [1, 10, 10, 10, 1]) == 32

assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 1, 3, 1, 3], energyDrinkB = [3, 1, 3, 1, 3, 1]) == 12

assert Solution().maxEnergyBoost(energyDrinkA = [5, 3, 8, 6, 2], energyDrinkB = [4, 7, 1, 9, 5]) == 26

assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 2, 2, 2, 3, 3, 3], energyDrinkB = [3, 3, 3, 2, 2, 2, 1, 1, 1]) == 22

assert Solution().maxEnergyBoost(energyDrinkA = [1,10,1,10,1,10], energyDrinkB = [10,1,10,1,10,1]) == 33

assert Solution().maxEnergyBoost(energyDrinkA = [1,1,2,2,3,3], energyDrinkB = [3,3,2,2,1,1]) == 14

assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 20, 10], energyDrinkB = [1, 2, 3, 2, 1]) == 90

assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 1, 2, 3, 1, 2, 3], energyDrinkB = [3, 2, 1, 3, 2, 1, 3, 2, 1]) == 18

assert Solution().maxEnergyBoost(energyDrinkA = [5, 2, 7, 8, 10], energyDrinkB = [3, 6, 1, 9, 4]) == 32

assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 4, 5], energyDrinkB = [5, 4, 3, 2, 1]) == 18

assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5], energyDrinkB = [3, 3, 3, 3, 3]) == 25

assert Solution().maxEnergyBoost(energyDrinkA = [2, 2, 2, 2, 2], energyDrinkB = [3, 1, 4, 1, 5]) == 14

assert Solution().maxEnergyBoost(energyDrinkA = [9, 8, 7, 6, 5, 4, 3, 2, 1], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 60

assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5,5,5], energyDrinkB = [5,5,5,5,5]) == 25

assert Solution().maxEnergyBoost(energyDrinkA = [1,1,1,100,100], energyDrinkB = [100,100,1,1,1]) == 400

assert Solution().maxEnergyBoost(energyDrinkA = [5, 3, 8, 6, 2], energyDrinkB = [2, 6, 3, 8, 5]) == 24

assert Solution().maxEnergyBoost(energyDrinkA = [5, 15, 25, 35, 45, 55], energyDrinkB = [55, 45, 35, 25, 15, 5]) == 235

assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 40, 50], energyDrinkB = [50, 40, 30, 20, 10]) == 180

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,1,1,1,1,1], energyDrinkB = [1,1,1,1,1,1]) == 6

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,100000,1], energyDrinkB = [100000,1,100000]) == 200001

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [4,1,1], energyDrinkB = [1,1,3]) == 7

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5,5], energyDrinkB = [1,1,1,1]) == 20

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5], energyDrinkB = [5,5,5]) == 15

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10,20,30], energyDrinkB = [30,20,10]) == 60

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000,100000,100000], energyDrinkB = [100000,100000,100000]) == 300000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5,5], energyDrinkB = [5,5,5,5]) == 20

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000,100000,100000], energyDrinkB = [1,1,1]) == 300000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,1,1,1,1,1,1,1,1,1], energyDrinkB = [2,2,2,2,2,2,2,2,2,2]) == 20

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5,6,7], energyDrinkB = [3,2,1]) == 18

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,2,3,4,5], energyDrinkB = [5,4,3,2,1]) == 18

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,3,1], energyDrinkB = [3,1,1]) == 5

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [3,2,5,10,7], energyDrinkB = [8,4,1,9,6]) == 30

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 20000, 30000, 40000, 10000], energyDrinkB = [10000, 40000, 20000, 30000, 50000]) == 150000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5], energyDrinkB = [10, 10, 10, 10, 10]) == 50

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000], energyDrinkB = [50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000]) == 500000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 5, 7, 9], energyDrinkB = [2, 4, 6, 8, 10]) == 30

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], energyDrinkB = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 200

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 50000, 50000, 50000, 50000], energyDrinkB = [100000, 100000, 100000, 100000, 100000]) == 500000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5], energyDrinkB = [1, 2, 3, 4, 5]) == 25

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [3, 5, 1, 7, 2, 8, 4, 6, 9, 0], energyDrinkB = [0, 9, 6, 4, 8, 2, 7, 1, 5, 3]) == 46

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [99999, 1, 99999, 1, 99999], energyDrinkB = [2, 99999, 2, 99999, 2]) == 299999

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], energyDrinkB = [90, 80, 70, 60, 50, 40, 30, 20, 10, 1]) == 700

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 2, 3, 4, 5, 6, 7, 8, 9, 10], energyDrinkB = [1, 9, 2, 8, 3, 7, 4, 6, 5, 1]) == 64

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], energyDrinkB = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 168

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,2,3,4,5,6,7,8,9,10], energyDrinkB = [10,9,8,7,6,5,4,3,2,1]) == 74

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 200, 300, 400, 500], energyDrinkB = [50, 100, 150, 200, 250]) == 1500

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], energyDrinkB = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 110

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [2, 3, 4, 5, 6, 7, 8, 9, 10, 1], energyDrinkB = [10, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == 60

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10,20,30,40,50], energyDrinkB = [50,40,30,20,10]) == 180

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,3,1,3,1,3,1,3,1,3], energyDrinkB = [3,1,3,1,3,1,3,1,3,1]) == 20

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11], energyDrinkB = [11, 10, 9, 8, 7, 6, 5, 4, 3, 2]) == 83

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3], energyDrinkB = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 60

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 2, 4, 5, 6], energyDrinkB = [6, 5, 4, 3, 2, 1]) == 26

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 1, 1, 1, 10], energyDrinkB = [1, 10, 10, 10, 1]) == 32

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 1, 100, 1, 100, 1, 100, 1, 100, 1], energyDrinkB = [1, 100, 1, 100, 1, 100, 1, 100, 1, 100]) == 505

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000, 100000, 100000, 100000, 100000], energyDrinkB = [50000, 50000, 50000, 50000, 50000]) == 500000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 100000], energyDrinkB = [100000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 200017

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], energyDrinkB = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]) == 180

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], energyDrinkB = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]) == 7400

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 1, 3, 1, 3], energyDrinkB = [3, 1, 3, 1, 3, 1]) == 12

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000, 1, 100000, 1, 100000, 1, 100000, 1, 100000, 1], energyDrinkB = [1, 100000, 1, 100000, 1, 100000, 1, 100000, 1, 100000]) == 500005

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 3, 8, 6, 2], energyDrinkB = [4, 7, 1, 9, 5]) == 26

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 1, 100, 1, 100, 1, 100], energyDrinkB = [1, 100, 1, 100, 1, 100, 1]) == 403

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 2, 2, 2, 3, 3, 3], energyDrinkB = [3, 3, 3, 2, 2, 2, 1, 1, 1]) == 22

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], energyDrinkB = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 116

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], energyDrinkB = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 299

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 1, 1, 1, 1, 1, 1, 100000], energyDrinkB = [100000, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 200007

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,10,1,10,1,10], energyDrinkB = [10,1,10,1,10,1]) == 33

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,1,2,2,3,3], energyDrinkB = [3,3,2,2,1,1]) == 14

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500], energyDrinkB = [500, 450, 400, 350, 300, 250, 200, 150, 100, 50]) == 3700

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 10000, 90000, 60000, 20000], energyDrinkB = [20000, 80000, 30000, 40000, 90000]) == 260000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 550

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], energyDrinkB = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 100

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [25000, 25000, 25000, 25000, 25000, 25000, 25000, 25000, 25000, 25000], energyDrinkB = [50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000]) == 500000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 50001, 50002, 50003, 50004, 50005, 50006, 50007, 50008, 50009], energyDrinkB = [50009, 50008, 50007, 50006, 50005, 50004, 50003, 50002, 50001, 50000]) == 500045

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 20, 10], energyDrinkB = [1, 2, 3, 2, 1]) == 90

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], energyDrinkB = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 65

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 1, 2, 3, 1, 2, 3], energyDrinkB = [3, 2, 1, 3, 2, 1, 3, 2, 1]) == 18

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 100000, 1, 100000, 1, 100000, 1, 100000, 1, 100000], energyDrinkB = [100000, 1, 100000, 1, 100000, 1, 100000, 1, 100000, 1]) == 500005

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 2, 7, 8, 10], energyDrinkB = [3, 6, 1, 9, 4]) == 32

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7], energyDrinkB = [2, 4, 3, 5, 4, 6, 5, 7, 6, 8]) == 50

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 74

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 999955

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 200, 300, 400, 500, 600], energyDrinkB = [600, 500, 400, 300, 200, 100]) == 2600

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 4, 5], energyDrinkB = [5, 4, 3, 2, 1]) == 18

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], energyDrinkB = [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]) == 1500000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2], energyDrinkB = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == 15

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 50, 100, 50, 100, 50, 100, 50], energyDrinkB = [50, 100, 50, 100, 50, 100, 50, 100]) == 600

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5], energyDrinkB = [3, 3, 3, 3, 3]) == 25

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [2, 2, 2, 2, 2], energyDrinkB = [3, 1, 4, 1, 5]) == 14

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], energyDrinkB = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 20

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [9, 8, 7, 6, 5, 4, 3, 2, 1], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 60

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7], energyDrinkB = [7, 5, 6, 4, 5, 3, 4, 2, 3, 1]) == 49

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], energyDrinkB = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 740

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5,5,5,5,5], energyDrinkB = [5,5,5,5,5]) == 25

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1,1,1,100,100], energyDrinkB = [100,100,1,1,1]) == 400

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 4, 5, 6, 7, 8, 9, 100000], energyDrinkB = [100000, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 200054

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000, 1, 100000, 1, 100000], energyDrinkB = [1, 100000, 1, 100000, 1]) == 300002

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3], energyDrinkB = [3, 1, 3, 1, 3, 1, 3, 1, 3, 1]) == 20

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 1, 1, 1, 1, 100000, 100000, 100000, 100000, 100000], energyDrinkB = [100000, 100000, 100000, 100000, 100000, 1, 1, 1, 1, 1]) == 900000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [90000, 90000, 90000, 90000, 90000, 90000, 90000, 90000, 90000, 90000], energyDrinkB = [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000]) == 900000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000], energyDrinkB = [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]) == 1000000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5], energyDrinkB = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == 36

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000, 90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 550000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100000, 1, 1, 1, 1, 1, 1, 1, 1, 1], energyDrinkB = [1, 1, 1, 1, 1, 1, 1, 1, 1, 100000]) == 200007

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5], energyDrinkB = [5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2]) == 60

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 3, 8, 6, 2], energyDrinkB = [2, 6, 3, 8, 5]) == 24

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], energyDrinkB = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 50

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], energyDrinkB = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 74

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100,100,100,100,100,100], energyDrinkB = [99,99,99,99,99,99]) == 600

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], energyDrinkB = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 100

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [5, 15, 25, 35, 45, 55], energyDrinkB = [55, 45, 35, 25, 15, 5]) == 235

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [1, 10, 100, 1000, 10000], energyDrinkB = [10000, 1000, 100, 10, 1]) == 22000

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], energyDrinkB = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 100

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [10, 20, 30, 40, 50], energyDrinkB = [50, 40, 30, 20, 10]) == 180

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [100, 1, 1, 1, 1, 1, 1, 1, 1, 100], energyDrinkB = [1, 100, 1, 1, 1, 1, 1, 100, 1, 1]) == 306

Answer: assert Solution().maxEnergyBoost(energyDrinkA = [50000, 90000, 30000, 70000, 60000, 20000, 80000, 40000, 10000, 100000], energyDrinkB = [100000, 10000, 80000, 20000, 40000, 60000, 10000, 70000, 50000, 30000]) == 550000

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def maxEnergyBoost(self, energyDrinkA: List[int], energyDrinkB: List[int]) -> int:
        n = len(energyDrinkA)
        f = [[0] * 2 for _ in range(n)]
        f[0][0] = energyDrinkA[0]
        f[0][1] = energyDrinkB[0]
        for i in range(1, n):
            f[i][0] = max(f[i - 1][0] + energyDrinkA[i], f[i - 1][1])
            f[i][1] = max(f[i - 1][1] + energyDrinkB[i], f[i - 1][0])
        return max(f[n - 1])


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
Given 2 integer arrays nums1 and nums2 consisting only of 0 and 1, your task is to calculate the minimum possible largest number in arrays nums1 and nums2, after doing the following.
Replace every 0 with an even positive integer and every 1 with an odd positive integer. After replacement, both arrays should be increasing and each integer should be used at most once.
Return the minimum possible largest number after applying the changes.

Example 1:

Input: nums1 = [], nums2 = [1,0,1,1]
Output: 5
Explanation:
After replacing, nums1 = [], and nums2 = [1, 2, 3, 5].

Example 2:

Input: nums1 = [0,1,0,1], nums2 = [1,0,0,1]
Output: 9
Explanation:
One way to replace, having 9 as the largest element is nums1 = [2, 3, 8, 9], and nums2 = [1, 4, 6, 7].

Example 3:

Input: nums1 = [0,1,0,0,1], nums2 = [0,0,0,1]
Output: 13
Explanation:
One way to replace, having 13 as the largest element is nums1 = [2, 3, 4, 6, 7], and nums2 = [8, 10, 12, 13].

Constraints:

0 <= nums1.length <= 1000
1 <= nums2.length <= 1000
nums1 and nums2 consist only of 0 and 1.

Your solution to the problem should be a method of the class Solution called minLargest and should pass all tests. Use the following starter code:
```python
class Solution:
    def minLargest(self, nums1: List[int], nums2: List[int]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
Given 2 integer arrays nums1 and nums2 consisting only of 0 and 1, your task is to calculate the minimum possible largest number in arrays nums1 and nums2, after doing the following.
Replace every 0 with an even positive integer and every 1 with an odd positive integer. After replacement, both arrays should be increasing and each integer should be used at most once.
Return the minimum possible largest number after applying the changes.

Example 1:

Input: nums1 = [], nums2 = [1,0,1,1]
Output: 5
Explanation:
After replacing, nums1 = [], and nums2 = [1, 2, 3, 5].

Example 2:

Input: nums1 = [0,1,0,1], nums2 = [1,0,0,1]
Output: 9
Explanation:
One way to replace, having 9 as the largest element is nums1 = [2, 3, 8, 9], and nums2 = [1, 4, 6, 7].

Example 3:

Input: nums1 = [0,1,0,0,1], nums2 = [0,0,0,1]
Output: 13
Explanation:
One way to replace, having 13 as the largest element is nums1 = [2, 3, 4, 6, 7], and nums2 = [8, 10, 12, 13].

Constraints:

0 <= nums1.length <= 1000
1 <= nums2.length <= 1000
nums1 and nums2 consist only of 0 and 1.

Your solution to the problem should be a method of the class Solution called minLargest and should pass all tests. Use the following starter code:
```python
class Solution:
    def minLargest(self, nums1: List[int], nums2: List[int]) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().minLargest(nums1 = [0,0,0,0], nums2 = [1,1,1,1]) == 8

assert Solution().minLargest(nums1 = [1], nums2 = [0]) == 2

assert Solution().minLargest(nums1 = [], nums2 = [0,0,0,0]) == 8

assert Solution().minLargest(nums1 = [1,0,1,0], nums2 = [0,1,0,1]) == 8

assert Solution().minLargest(nums1 = [1,1], nums2 = [1,1]) == 7

assert Solution().minLargest(nums1 = [1,0], nums2 = [0,1]) == 4

assert Solution().minLargest(nums1 = [0,0], nums2 = [1,1]) == 4

assert Solution().minLargest(nums1 = [0,0], nums2 = [0,0]) == 8

assert Solution().minLargest(nums1 = [0,0,1,1], nums2 = [1,1,0,0]) == 8

assert Solution().minLargest(nums1 = [], nums2 = []) == 0

assert Solution().minLargest(nums1 = [], nums2 = [0]) == 2

assert Solution().minLargest(nums1 = [], nums2 = [1,0,1,1]) == 5

assert Solution().minLargest(nums1 = [1,1,1,1], nums2 = []) == 7

assert Solution().minLargest(nums1 = [1,0,1,0], nums2 = [0,1]) == 6

assert Solution().minLargest(nums1 = [0,1,0,1], nums2 = [1,0,0,1]) == 9

assert Solution().minLargest(nums1 = [0,0,0], nums2 = [1,1,1]) == 6

assert Solution().minLargest(nums1 = [1,0,0], nums2 = [0,1,1]) == 6

assert Solution().minLargest(nums1 = [0], nums2 = [1]) == 2

assert Solution().minLargest(nums1 = [0,1], nums2 = [1,0,1,0]) == 6

assert Solution().minLargest(nums1 = [1,0,1], nums2 = [0,1,0]) == 6

assert Solution().minLargest(nums1 = [1,1,1], nums2 = [0,0,0]) == 6

assert Solution().minLargest(nums1 = [1,1], nums2 = [0,0]) == 4

assert Solution().minLargest(nums1 = [1], nums2 = []) == 1

Answer: assert Solution().minLargest(nums1 = [0,0,0,0], nums2 = [1,1,1,1]) == 8

Answer: assert Solution().minLargest(nums1 = [1], nums2 = [0]) == 2

Answer: assert Solution().minLargest(nums1 = [], nums2 = [0,0,0,0]) == 8

Answer: assert Solution().minLargest(nums1 = [1,0,1,0], nums2 = [0,1,0,1]) == 8

Answer: assert Solution().minLargest(nums1 = [1,1], nums2 = [1,1]) == 7

Answer: assert Solution().minLargest(nums1 = [1,0], nums2 = [0,1]) == 4

Answer: assert Solution().minLargest(nums1 = [0,0], nums2 = [1,1]) == 4

Answer: assert Solution().minLargest(nums1 = [0,0], nums2 = [0,0]) == 8

Answer: assert Solution().minLargest(nums1 = [0,0,1,1], nums2 = [1,1,0,0]) == 8

Answer: assert Solution().minLargest(nums1 = [], nums2 = []) == 0

Answer: assert Solution().minLargest(nums1 = [], nums2 = [0]) == 2

Answer: assert Solution().minLargest(nums1 = [], nums2 = [1,0,1,1]) == 5

Answer: assert Solution().minLargest(nums1 = [1,1,1,1], nums2 = []) == 7

Answer: assert Solution().minLargest(nums1 = [1,0,1,0], nums2 = [0,1]) == 6

Answer: assert Solution().minLargest(nums1 = [0,1,0,1], nums2 = [1,0,0,1]) == 9

Answer: assert Solution().minLargest(nums1 = [0,0,0], nums2 = [1,1,1]) == 6

Answer: assert Solution().minLargest(nums1 = [1,0,0], nums2 = [0,1,1]) == 6

Answer: assert Solution().minLargest(nums1 = [0,1,0,0,1], nums2 = [0,0,0,1]) == 13

Answer: assert Solution().minLargest(nums1 = [0], nums2 = [1]) == 2

Answer: assert Solution().minLargest(nums1 = [0,1], nums2 = [1,0,1,0]) == 6

Answer: assert Solution().minLargest(nums1 = [1,0,1], nums2 = [0,1,0]) == 6

Answer: assert Solution().minLargest(nums1 = [1,1,1], nums2 = [0,0,0]) == 6

Answer: assert Solution().minLargest(nums1 = [1,1], nums2 = [0,0]) == 4

Answer: assert Solution().minLargest(nums1 = [1], nums2 = []) == 1

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0], nums2 = [1,1,1,1,1,1]) == 12

Answer: assert Solution().minLargest(nums1 = [1,0,0,1,0,0,1,0,0,1], nums2 = [0,1,1,0,1,1,0,1,1,0]) == 20

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0]) == 16

Answer: assert Solution().minLargest(nums1 = [1, 1, 0, 0, 1, 0, 1], nums2 = [0, 1, 1, 0, 0, 1, 1]) == 15

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0]) == 14

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 40

Answer: assert Solution().minLargest(nums1 = [1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0], nums2 = [0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1]) == 32

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1,0,0,0,0,0,0], nums2 = [0,0,0,0,0,0,1,1,1,1,1,1]) == 24

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]) == 44

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1], nums2 = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]) == 22

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1]) == 18

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 41

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0]) == 28

Answer: assert Solution().minLargest(nums1 = [1, 0, 1, 0, 1, 0, 1, 0, 1], nums2 = [0]) == 10

Answer: assert Solution().minLargest(nums1 = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0], nums2 = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 20

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 1, 1, 1, 1], nums2 = [1, 1, 1, 1, 0, 0, 0, 0]) == 16

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1], nums2 = [0,0,0,0,0]) == 10

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0], nums2 = [1,0,1,0,1,0,1]) == 14

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1,1,1]) == 24

Answer: assert Solution().minLargest(nums1 = [1,0,0,0,1,0,0,0], nums2 = [0,1,1,1,0,1,1,1]) == 16

Answer: assert Solution().minLargest(nums1 = [1,0,0,1,0,0,1,0], nums2 = [0,1,1,0,1,1,0,1]) == 16

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], nums2 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]) == 32

Answer: assert Solution().minLargest(nums1 = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], nums2 = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 22

Answer: assert Solution().minLargest(nums1 = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1], nums2 = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 20

Answer: assert Solution().minLargest(nums1 = [], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 29

Answer: assert Solution().minLargest(nums1 = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1], nums2 = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 20

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1], nums2 = [0,1,0,1,0,1]) == 13

Answer: assert Solution().minLargest(nums1 = [1,0,0,0,0,1,1,0], nums2 = [0,1,0,1,0,1,0,1]) == 19

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1]) == 15

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 20

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0,1,0], nums2 = [0,1,0,1,0,1,0,1,0,1,0,1]) == 24

Answer: assert Solution().minLargest(nums1 = [1, 0, 1, 0, 1, 0, 1, 0, 1], nums2 = [0, 1, 0, 1, 0, 1, 0, 1, 0]) == 18

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 40

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1,1]) == 21

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0]) == 18

Answer: assert Solution().minLargest(nums1 = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], nums2 = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 24

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]) == 40

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0]) == 24

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0,1], nums2 = [0,1,0,1,0,1,0,1,0,1]) == 21

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0], nums2 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]) == 64

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 40

Answer: assert Solution().minLargest(nums1 = [0], nums2 = [1,0,1,0,1,0,1,0,1,0]) == 12

Answer: assert Solution().minLargest(nums1 = [0, 1, 0, 1, 0, 1, 0], nums2 = [1, 0, 1, 0, 1, 0, 1]) == 14

Answer: assert Solution().minLargest(nums1 = [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0], nums2 = [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1]) == 32

Answer: assert Solution().minLargest(nums1 = [0,1,1,0,0,1,0,1,0,1], nums2 = [1,0,0,1,0,0,1,0,0,1]) == 23

Answer: assert Solution().minLargest(nums1 = [0,0,1,1,1,0,0,1,1,1], nums2 = [1,1,0,0,0,1,1,0,0,0]) == 20

Answer: assert Solution().minLargest(nums1 = [1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0], nums2 = [0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1]) == 40

Answer: assert Solution().minLargest(nums1 = [0, 1, 1, 0, 1, 0], nums2 = [1, 0, 0, 1, 0]) == 12

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0], nums2 = [0,1,0,1,0,1,0,1,0,1]) == 20

Answer: assert Solution().minLargest(nums1 = [0,0,1,1,1,0], nums2 = [1,0,0,0,1]) == 12

Answer: assert Solution().minLargest(nums1 = [0], nums2 = [1, 0, 1, 0, 1, 0, 1, 0, 1]) == 10

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1], nums2 = [0,0,0,0,0,0]) == 12

Answer: assert Solution().minLargest(nums1 = [0,1,1,1,0,1,0,0,1,0], nums2 = [1,0,0,1,1,0,1,0,0,1]) == 20

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0], nums2 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]) == 32

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 30

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,1,1,1,1], nums2 = [1,1,0,0,0,0,1,1]) == 19

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1,1,1,1,1,1,1], nums2 = [0,0,0,0,0,0,0,0,0,0,0,0]) == 24

Answer: assert Solution().minLargest(nums1 = [0,0,1,1,0,0,1,1,0,0], nums2 = [1,1,0,0,1,1,0,0,1,1]) == 20

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], nums2 = []) == 30

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0], nums2 = [1,1,1,1,1]) == 10

Answer: assert Solution().minLargest(nums1 = [1,1,1,0,0,1,1,1,0,0], nums2 = [0,0,1,1,1,0,0,1,1,1]) == 23

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], nums2 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]) == 40

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0], nums2 = [0,1,0,1,0,1,0,1]) == 16

Answer: assert Solution().minLargest(nums1 = [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0], nums2 = [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1]) == 40

Answer: assert Solution().minLargest(nums1 = [0,1,1,0,0,1,1,0,0,1], nums2 = [1,0,0,1,1,0,0,1,1,0]) == 20

Answer: assert Solution().minLargest(nums1 = [0,0,1,1,0,0,1,1,0,0,1,1], nums2 = [1,1,0,0,1,1,0,0,1,1,0,0]) == 24

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 20

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]) == 65

Answer: assert Solution().minLargest(nums1 = [1, 0, 1, 0, 1, 0], nums2 = [0, 1, 0, 1, 0, 1]) == 12

Answer: assert Solution().minLargest(nums1 = [0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,0], nums2 = [1,0,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]) == 52

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1], nums2 = [0,1,0,1,0,1,0]) == 14

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 1, 1], nums2 = [0, 0, 0, 0, 0]) == 10

Answer: assert Solution().minLargest(nums1 = [1,1,0,0,1,1,0,0,1,1,0,0,1,1], nums2 = [0,0,1,1,0,0,1,1,0,0,1,1,0,0]) == 28

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 0, 0, 0, 1, 1], nums2 = [0, 0, 0, 1, 1, 1, 0, 0]) == 16

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1], nums2 = [1,0,1,0,1]) == 11

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 32

Answer: assert Solution().minLargest(nums1 = [0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1], nums2 = [1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0]) == 64

Answer: assert Solution().minLargest(nums1 = [0, 1, 0, 1, 0, 1, 0, 1], nums2 = [1, 0, 1, 0, 1, 0, 1, 0]) == 16

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]) == 32

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]) == 91

Answer: assert Solution().minLargest(nums1 = [1,0,0,1,0,1,0,1], nums2 = [0,1,1,0,1,0,1,0]) == 16

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], nums2 = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]) == 44

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1], nums2 = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]) == 22

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 30

Answer: assert Solution().minLargest(nums1 = [1,1,0,0,1,0], nums2 = [0,0,1,1,0,1,1,0]) == 14

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1,1,1,1,1,1], nums2 = [0,0,0,0,0,0,0,0,0,0]) == 20

Answer: assert Solution().minLargest(nums1 = [1, 1, 1, 0, 0, 0, 1, 1, 1], nums2 = [0, 0, 0, 1, 1, 1, 0, 0, 0]) == 18

Answer: assert Solution().minLargest(nums1 = [1,0,0,1,1,0,0,1,1,0,0], nums2 = [0,1,1,0,0,1,1,0,0,1,1]) == 22

Answer: assert Solution().minLargest(nums1 = [0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1]) == 33

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0,1], nums2 = [0,1,0,1,0,1,0,1,0,1,0]) == 22

Answer: assert Solution().minLargest(nums1 = [1,1,1,1,1], nums2 = [0,0,0,0,0,0,0,0]) == 16

Answer: assert Solution().minLargest(nums1 = [0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0], nums2 = [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]) == 40

Answer: assert Solution().minLargest(nums1 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1], nums2 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]) == 63

Answer: assert Solution().minLargest(nums1 = [0, 0, 0, 0, 0], nums2 = [1, 1, 1, 1, 1]) == 10

Answer: assert Solution().minLargest(nums1 = [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0], nums2 = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]) == 40

Answer: assert Solution().minLargest(nums1 = [0,0,0,0,0,0,0,0,0,0], nums2 = [1,1,1,1,1,1,1,1,1,1]) == 20

Answer: assert Solution().minLargest(nums1 = [1,0,0,0,1,0,0,0,1,0,0,0], nums2 = [0,0,0,1,0,0,0,1,0,0,0,1]) == 36

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def minLargest(self, nums1: List[int], nums2: List[int]) -> int:
        def nxt(x: int, y: int) -> int:
            return x + 1 if (x & 1 ^ y) == 1 else x + 2

        m, n = len(nums1), len(nums2)
        f = [[0] * (n + 1) for _ in range(m + 1)]
        for i, x in enumerate(nums1, 1):
            f[i][0] = nxt(f[i - 1][0], x)
        for j, y in enumerate(nums2, 1):
            f[0][j] = nxt(f[0][j - 1], y)
        for i, x in enumerate(nums1, 1):
            for j, y in enumerate(nums2, 1):
                f[i][j] = min(nxt(f[i - 1][j], x), nxt(f[i][j - 1], y))
        return f[m][n]


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given two positive integers n and k.
An integer x is called k-palindromic if:

x is a palindrome.
x is divisible by k.

An integer is called good if its digits can be rearranged to form a k-palindromic integer. For example, for k = 2, 2020 can be rearranged to form the k-palindromic integer 2002, whereas 1010 cannot be rearranged to form a k-palindromic integer.
Return the count of good integers containing n digits.
Note that any integer must not have leading zeros, neither before nor after rearrangement. For example, 1010 cannot be rearranged to form 101.

Example 1:

Input: n = 3, k = 5
Output: 27
Explanation:
Some of the good integers are:

551 because it can be rearranged to form 515.
525 because it is already k-palindromic.

Example 2:

Input: n = 1, k = 4
Output: 2
Explanation:
The two good integers are 4 and 8.

Example 3:

Input: n = 5, k = 6
Output: 2468

Constraints:

1 <= n <= 10
1 <= k <= 9

Your solution to the problem should be a method of the class Solution called countGoodIntegers and should pass all tests. Use the following starter code:
```python
class Solution:
    def countGoodIntegers(self, n: int, k: int) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given two positive integers n and k.
An integer x is called k-palindromic if:

x is a palindrome.
x is divisible by k.

An integer is called good if its digits can be rearranged to form a k-palindromic integer. For example, for k = 2, 2020 can be rearranged to form the k-palindromic integer 2002, whereas 1010 cannot be rearranged to form a k-palindromic integer.
Return the count of good integers containing n digits.
Note that any integer must not have leading zeros, neither before nor after rearrangement. For example, 1010 cannot be rearranged to form 101.

Example 1:

Input: n = 3, k = 5
Output: 27
Explanation:
Some of the good integers are:

551 because it can be rearranged to form 515.
525 because it is already k-palindromic.

Example 2:

Input: n = 1, k = 4
Output: 2
Explanation:
The two good integers are 4 and 8.

Example 3:

Input: n = 5, k = 6
Output: 2468

Constraints:

1 <= n <= 10
1 <= k <= 9

Your solution to the problem should be a method of the class Solution called countGoodIntegers and should pass all tests. Use the following starter code:
```python
class Solution:
    def countGoodIntegers(self, n: int, k: int) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().countGoodIntegers(n = 6, k = 8) == 5221

assert Solution().countGoodIntegers(n = 10, k = 9) == 4610368

assert Solution().countGoodIntegers(n = 1, k = 4) == 2

assert Solution().countGoodIntegers(n = 6, k = 9) == 1248

assert Solution().countGoodIntegers(n = 9, k = 1) == 41457015

assert Solution().countGoodIntegers(n = 8, k = 2) == 563392

assert Solution().countGoodIntegers(n = 10, k = 5) == 19284856

assert Solution().countGoodIntegers(n = 3, k = 5) == 27

assert Solution().countGoodIntegers(n = 8, k = 5) == 237112

assert Solution().countGoodIntegers(n = 9, k = 2) == 37728000

assert Solution().countGoodIntegers(n = 2, k = 3) == 3

assert Solution().countGoodIntegers(n = 10, k = 2) == 39718144

assert Solution().countGoodIntegers(n = 4, k = 3) == 84

assert Solution().countGoodIntegers(n = 6, k = 7) == 3044

assert Solution().countGoodIntegers(n = 5, k = 6) == 2468

assert Solution().countGoodIntegers(n = 2, k = 2) == 4

assert Solution().countGoodIntegers(n = 4, k = 7) == 76

assert Solution().countGoodIntegers(n = 7, k = 9) == 68739

assert Solution().countGoodIntegers(n = 6, k = 2) == 9064

assert Solution().countGoodIntegers(n = 7, k = 8) == 292692

assert Solution().countGoodIntegers(n = 9, k = 4) == 33175696

assert Solution().countGoodIntegers(n = 4, k = 8) == 52

assert Solution().countGoodIntegers(n = 4, k = 9) == 28

assert Solution().countGoodIntegers(n = 9, k = 5) == 15814071

assert Solution().countGoodIntegers(n = 7, k = 3) == 206217

assert Solution().countGoodIntegers(n = 9, k = 8) == 30771543

assert Solution().countGoodIntegers(n = 5, k = 1) == 10935

assert Solution().countGoodIntegers(n = 4, k = 5) == 52

assert Solution().countGoodIntegers(n = 10, k = 3) == 13831104

assert Solution().countGoodIntegers(n = 7, k = 2) == 509248

assert Solution().countGoodIntegers(n = 5, k = 9) == 1191

assert Solution().countGoodIntegers(n = 5, k = 2) == 7400

assert Solution().countGoodIntegers(n = 3, k = 9) == 23

assert Solution().countGoodIntegers(n = 10, k = 6) == 13249798

assert Solution().countGoodIntegers(n = 7, k = 4) == 393948

assert Solution().countGoodIntegers(n = 5, k = 7) == 2665

assert Solution().countGoodIntegers(n = 8, k = 3) == 207840

assert Solution().countGoodIntegers(n = 8, k = 4) == 494818

assert Solution().countGoodIntegers(n = 6, k = 4) == 6992

assert Solution().countGoodIntegers(n = 2, k = 9) == 1

assert Solution().countGoodIntegers(n = 8, k = 7) == 506388

assert Solution().countGoodIntegers(n = 9, k = 3) == 13726509

assert Solution().countGoodIntegers(n = 4, k = 2) == 172

assert Solution().countGoodIntegers(n = 5, k = 5) == 2231

assert Solution().countGoodIntegers(n = 9, k = 6) == 12476696

assert Solution().countGoodIntegers(n = 5, k = 3) == 3573

assert Solution().countGoodIntegers(n = 9, k = 7) == 36789447

assert Solution().countGoodIntegers(n = 3, k = 8) == 27

assert Solution().countGoodIntegers(n = 3, k = 1) == 243

assert Solution().countGoodIntegers(n = 6, k = 3) == 3744

assert Solution().countGoodIntegers(n = 6, k = 6) == 3109

assert Solution().countGoodIntegers(n = 5, k = 8) == 2231

assert Solution().countGoodIntegers(n = 4, k = 6) == 58

assert Solution().countGoodIntegers(n = 8, k = 8) == 460048

assert Solution().countGoodIntegers(n = 6, k = 5) == 3256

assert Solution().countGoodIntegers(n = 10, k = 7) == 40242031

Answer: assert Solution().countGoodIntegers(n = 6, k = 8) == 5221

Answer: assert Solution().countGoodIntegers(n = 10, k = 9) == 4610368

Answer: assert Solution().countGoodIntegers(n = 1, k = 4) == 2

Answer: assert Solution().countGoodIntegers(n = 6, k = 9) == 1248

Answer: assert Solution().countGoodIntegers(n = 9, k = 1) == 41457015

Answer: assert Solution().countGoodIntegers(n = 8, k = 2) == 563392

Answer: assert Solution().countGoodIntegers(n = 10, k = 5) == 19284856

Answer: assert Solution().countGoodIntegers(n = 3, k = 5) == 27

Answer: assert Solution().countGoodIntegers(n = 8, k = 5) == 237112

Answer: assert Solution().countGoodIntegers(n = 9, k = 2) == 37728000

Answer: assert Solution().countGoodIntegers(n = 2, k = 3) == 3

Answer: assert Solution().countGoodIntegers(n = 10, k = 2) == 39718144

Answer: assert Solution().countGoodIntegers(n = 4, k = 3) == 84

Answer: assert Solution().countGoodIntegers(n = 6, k = 7) == 3044

Answer: assert Solution().countGoodIntegers(n = 5, k = 6) == 2468

Answer: assert Solution().countGoodIntegers(n = 2, k = 2) == 4

Answer: assert Solution().countGoodIntegers(n = 4, k = 7) == 76

Answer: assert Solution().countGoodIntegers(n = 7, k = 9) == 68739

Answer: assert Solution().countGoodIntegers(n = 6, k = 2) == 9064

Answer: assert Solution().countGoodIntegers(n = 7, k = 8) == 292692

Answer: assert Solution().countGoodIntegers(n = 9, k = 4) == 33175696

Answer: assert Solution().countGoodIntegers(n = 4, k = 8) == 52

Answer: assert Solution().countGoodIntegers(n = 4, k = 9) == 28

Answer: assert Solution().countGoodIntegers(n = 9, k = 5) == 15814071

Answer: assert Solution().countGoodIntegers(n = 7, k = 3) == 206217

Answer: assert Solution().countGoodIntegers(n = 9, k = 8) == 30771543

Answer: assert Solution().countGoodIntegers(n = 5, k = 1) == 10935

Answer: assert Solution().countGoodIntegers(n = 4, k = 5) == 52

Answer: assert Solution().countGoodIntegers(n = 10, k = 3) == 13831104

Answer: assert Solution().countGoodIntegers(n = 7, k = 2) == 509248

Answer: assert Solution().countGoodIntegers(n = 5, k = 9) == 1191

Answer: assert Solution().countGoodIntegers(n = 5, k = 2) == 7400

Answer: assert Solution().countGoodIntegers(n = 3, k = 9) == 23

Answer: assert Solution().countGoodIntegers(n = 10, k = 6) == 13249798

Answer: assert Solution().countGoodIntegers(n = 7, k = 4) == 393948

Answer: assert Solution().countGoodIntegers(n = 5, k = 7) == 2665

Answer: assert Solution().countGoodIntegers(n = 8, k = 3) == 207840

Answer: assert Solution().countGoodIntegers(n = 8, k = 4) == 494818

Answer: assert Solution().countGoodIntegers(n = 6, k = 4) == 6992

Answer: assert Solution().countGoodIntegers(n = 2, k = 9) == 1

Answer: assert Solution().countGoodIntegers(n = 8, k = 7) == 506388

Answer: assert Solution().countGoodIntegers(n = 9, k = 3) == 13726509

Answer: assert Solution().countGoodIntegers(n = 4, k = 2) == 172

Answer: assert Solution().countGoodIntegers(n = 5, k = 5) == 2231

Answer: assert Solution().countGoodIntegers(n = 9, k = 6) == 12476696

Answer: assert Solution().countGoodIntegers(n = 5, k = 3) == 3573

Answer: assert Solution().countGoodIntegers(n = 9, k = 7) == 36789447

Answer: assert Solution().countGoodIntegers(n = 3, k = 8) == 27

Answer: assert Solution().countGoodIntegers(n = 3, k = 1) == 243

Answer: assert Solution().countGoodIntegers(n = 6, k = 3) == 3744

Answer: assert Solution().countGoodIntegers(n = 6, k = 6) == 3109

Answer: assert Solution().countGoodIntegers(n = 5, k = 8) == 2231

Answer: assert Solution().countGoodIntegers(n = 4, k = 6) == 58

Answer: assert Solution().countGoodIntegers(n = 8, k = 8) == 460048

Answer: assert Solution().countGoodIntegers(n = 6, k = 5) == 3256

Answer: assert Solution().countGoodIntegers(n = 10, k = 7) == 40242031

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def countGoodIntegers(self, n: int, k: int) -> int:
        fac = [factorial(i) for i in range(n + 1)]
        ans = 0
        vis = set()
        base = 10 ** ((n - 1) // 2)
        for i in range(base, base * 10):
            s = str(i)
            s += s[::-1][n % 2 :]
            if int(s) % k:
                continue
            t = "".join(sorted(s))
            if t in vis:
                continue
            vis.add(t)
            cnt = Counter(t)
            res = (n - cnt["0"]) * fac[n - 1]
            for x in cnt.values():
                res //= fac[x]
            ans += res
        return ans


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given an integer power and two integer arrays damage and health, both having length n.
Bob has n enemies, where enemy i will deal Bob damage[i] points of damage per second while they are alive (i.e. health[i] > 0).
Every second, after the enemies deal damage to Bob, he chooses one of the enemies that is still alive and deals power points of damage to them.
Determine the minimum total amount of damage points that will be dealt to Bob before all n enemies are dead.

Example 1:

Input: power = 4, damage = [1,2,3,4], health = [4,5,6,8]
Output: 39
Explanation:

Attack enemy 3 in the first two seconds, after which enemy 3 will go down, the number of damage points dealt to Bob is 10 + 10 = 20 points.
Attack enemy 2 in the next two seconds, after which enemy 2 will go down, the number of damage points dealt to Bob is 6 + 6 = 12 points.
Attack enemy 0 in the next second, after which enemy 0 will go down, the number of damage points dealt to Bob is 3 points.
Attack enemy 1 in the next two seconds, after which enemy 1 will go down, the number of damage points dealt to Bob is 2 + 2 = 4 points.

Example 2:

Input: power = 1, damage = [1,1,1,1], health = [1,2,3,4]
Output: 20
Explanation:

Attack enemy 0 in the first second, after which enemy 0 will go down, the number of damage points dealt to Bob is 4 points.
Attack enemy 1 in the next two seconds, after which enemy 1 will go down, the number of damage points dealt to Bob is 3 + 3 = 6 points.
Attack enemy 2 in the next three seconds, after which enemy 2 will go down, the number of damage points dealt to Bob is 2 + 2 + 2 = 6 points.
Attack enemy 3 in the next four seconds, after which enemy 3 will go down, the number of damage points dealt to Bob is 1 + 1 + 1 + 1 = 4 points.

Example 3:

Input: power = 8, damage = [40], health = [59]
Output: 320

Constraints:

1 <= power <= 104
1 <= n == damage.length == health.length <= 105
1 <= damage[i], health[i] <= 104

Your solution to the problem should be a method of the class Solution called minDamage and should pass all tests. Use the following starter code:
```python
class Solution:
    def minDamage(self, power: int, damage: List[int], health: List[int]) -> int:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given an integer power and two integer arrays damage and health, both having length n.
Bob has n enemies, where enemy i will deal Bob damage[i] points of damage per second while they are alive (i.e. health[i] > 0).
Every second, after the enemies deal damage to Bob, he chooses one of the enemies that is still alive and deals power points of damage to them.
Determine the minimum total amount of damage points that will be dealt to Bob before all n enemies are dead.

Example 1:

Input: power = 4, damage = [1,2,3,4], health = [4,5,6,8]
Output: 39
Explanation:

Attack enemy 3 in the first two seconds, after which enemy 3 will go down, the number of damage points dealt to Bob is 10 + 10 = 20 points.
Attack enemy 2 in the next two seconds, after which enemy 2 will go down, the number of damage points dealt to Bob is 6 + 6 = 12 points.
Attack enemy 0 in the next second, after which enemy 0 will go down, the number of damage points dealt to Bob is 3 points.
Attack enemy 1 in the next two seconds, after which enemy 1 will go down, the number of damage points dealt to Bob is 2 + 2 = 4 points.

Example 2:

Input: power = 1, damage = [1,1,1,1], health = [1,2,3,4]
Output: 20
Explanation:

Attack enemy 0 in the first second, after which enemy 0 will go down, the number of damage points dealt to Bob is 4 points.
Attack enemy 1 in the next two seconds, after which enemy 1 will go down, the number of damage points dealt to Bob is 3 + 3 = 6 points.
Attack enemy 2 in the next three seconds, after which enemy 2 will go down, the number of damage points dealt to Bob is 2 + 2 + 2 = 6 points.
Attack enemy 3 in the next four seconds, after which enemy 3 will go down, the number of damage points dealt to Bob is 1 + 1 + 1 + 1 = 4 points.

Example 3:

Input: power = 8, damage = [40], health = [59]
Output: 320

Constraints:

1 <= power <= 104
1 <= n == damage.length == health.length <= 105
1 <= damage[i], health[i] <= 104

Your solution to the problem should be a method of the class Solution called minDamage and should pass all tests. Use the following starter code:
```python
class Solution:
    def minDamage(self, power: int, damage: List[int], health: List[int]) -> int:
        # Add your code here
```

SOLUTION:

assert Solution().minDamage(power = 2, damage = [1,1,1,1,1], health = [1,2,3,4,5]) == 22

assert Solution().minDamage(power = 4, damage = [1,2,3,4], health = [4,5,6,8]) == 39

assert Solution().minDamage(power = 5, damage = [3,2,1], health = [10,15,20]) == 25

assert Solution().minDamage(power = 5, damage = [2,3,4], health = [10,15,20]) == 55

assert Solution().minDamage(power = 10, damage = [5,5,5,5], health = [5,5,5,5]) == 50

assert Solution().minDamage(power = 10, damage = [1,1,1,1,1], health = [1,1,1,1,1]) == 15

assert Solution().minDamage(power = 10, damage = [5,5,5,5], health = [10,10,10,10]) == 50

assert Solution().minDamage(power = 3, damage = [2,2,2,2], health = [3,3,3,3]) == 20

assert Solution().minDamage(power = 5, damage = [3, 3, 3], health = [6, 6, 6]) == 36

assert Solution().minDamage(power = 100, damage = [5, 10, 15], health = [100, 200, 300]) == 125

assert Solution().minDamage(power = 1, damage = [1,1,1,1], health = [1,2,3,4]) == 20

assert Solution().minDamage(power = 8, damage = [40], health = [59]) == 320

assert Solution().minDamage(power = 5, damage = [2,3,1,4], health = [10,20,30,40]) == 98

assert Solution().minDamage(power = 10000, damage = [10000], health = [10000]) == 10000

Answer: assert Solution().minDamage(power = 2, damage = [1,1,1,1,1], health = [1,2,3,4,5]) == 22

Answer: assert Solution().minDamage(power = 100, damage = [10,20,30], health = [100,100,100]) == 100

Answer: assert Solution().minDamage(power = 4, damage = [1,2,3,4], health = [4,5,6,8]) == 39

Answer: assert Solution().minDamage(power = 5, damage = [3,2,1], health = [10,15,20]) == 25

Answer: assert Solution().minDamage(power = 100, damage = [50,50,50], health = [100,100,100]) == 300

Answer: assert Solution().minDamage(power = 5, damage = [2,3,4], health = [10,15,20]) == 55

Answer: assert Solution().minDamage(power = 10, damage = [5,5,5,5], health = [5,5,5,5]) == 50

Answer: assert Solution().minDamage(power = 10, damage = [1,1,1,1,1], health = [1,1,1,1,1]) == 15

Answer: assert Solution().minDamage(power = 10, damage = [5,5,5,5], health = [10,10,10,10]) == 50

Answer: assert Solution().minDamage(power = 3, damage = [2,2,2,2], health = [3,3,3,3]) == 20

Answer: assert Solution().minDamage(power = 5, damage = [3, 3, 3], health = [6, 6, 6]) == 36

Answer: assert Solution().minDamage(power = 5000, damage = [100,200,300,400], health = [5000,5000,5000,5000]) == 2000

Answer: assert Solution().minDamage(power = 100, damage = [5, 10, 15], health = [100, 200, 300]) == 125

Answer: assert Solution().minDamage(power = 100, damage = [10,20,30], health = [100,200,300]) == 250

Answer: assert Solution().minDamage(power = 1, damage = [1,1,1,1], health = [1,2,3,4]) == 20

Answer: assert Solution().minDamage(power = 5000, damage = [1,2,3], health = [10000,15000,20000]) == 35

Answer: assert Solution().minDamage(power = 8, damage = [40], health = [59]) == 320

Answer: assert Solution().minDamage(power = 1234, damage = [4321, 8642, 12963, 17284, 21605], health = [43210, 86420, 129630, 172840, 216050]) == 21324135

Answer: assert Solution().minDamage(power = 500, damage = [99,98,97,96,95], health = [1000,999,998,997,996]) == 2890

Answer: assert Solution().minDamage(power = 20, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 220

Answer: assert Solution().minDamage(power = 1, damage = [100, 200, 300, 400, 500], health = [500, 600, 700, 800, 900]) == 2800000

Answer: assert Solution().minDamage(power = 100, damage = [10, 20, 30, 40, 50], health = [100, 100, 100, 100, 100]) == 350

Answer: assert Solution().minDamage(power = 50, damage = [10, 20, 30, 40, 50], health = [50, 100, 150, 200, 250]) == 1400

Answer: assert Solution().minDamage(power = 7, damage = [2, 4, 6, 8, 10], health = [15, 25, 35, 45, 55]) == 468

Answer: assert Solution().minDamage(power = 100, damage = [99, 98, 97, 96, 95, 94, 93, 92, 91, 90], health = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 5115

Answer: assert Solution().minDamage(power = 1000, damage = [100, 200, 300, 400, 500], health = [900, 800, 700, 600, 500]) == 3500

Answer: assert Solution().minDamage(power = 600, damage = [15, 30, 45, 60, 75, 90, 105, 120], health = [1200, 1800, 2400, 3000, 3600, 4200, 4800, 5400]) == 13050

Answer: assert Solution().minDamage(power = 3, damage = [1, 2, 3, 4, 5], health = [10, 20, 30, 40, 50]) == 477

Answer: assert Solution().minDamage(power = 5000, damage = [1000, 2000, 3000, 4000, 5000], health = [5000, 5000, 5000, 5000, 5000]) == 35000

Answer: assert Solution().minDamage(power = 1, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 15400

Answer: assert Solution().minDamage(power = 100, damage = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100], health = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 7700

Answer: assert Solution().minDamage(power = 150, damage = [30, 60, 90, 120, 150, 180], health = [1200, 1500, 1800, 2100, 2400, 2700]) == 26040

Answer: assert Solution().minDamage(power = 123, damage = [100, 150, 200, 250, 300], health = [1000, 2000, 3000, 4000, 5000]) == 73500

Answer: assert Solution().minDamage(power = 500, damage = [100,200,300,400], health = [2000,3000,4000,5000]) == 17000

Answer: assert Solution().minDamage(power = 10000, damage = [5000, 5000, 5000, 5000, 5000], health = [10000, 10000, 10000, 10000, 10000]) == 75000

Answer: assert Solution().minDamage(power = 10000, damage = [10000,10000,10000,10000,10000], health = [10000,10000,10000,10000,10000]) == 150000

Answer: assert Solution().minDamage(power = 5000, damage = [1000, 2000, 3000, 4000, 5000], health = [10000, 20000, 30000, 40000, 50000]) == 280000

Answer: assert Solution().minDamage(power = 5, damage = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], health = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 341000

Answer: assert Solution().minDamage(power = 2000, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000]) == 220

Answer: assert Solution().minDamage(power = 10, damage = [10, 20, 30, 40, 50], health = [1, 2, 3, 4, 5]) == 350

Answer: assert Solution().minDamage(power = 500, damage = [100, 150, 200, 250, 300], health = [150, 200, 250, 300, 350]) == 2500

Answer: assert Solution().minDamage(power = 50, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 3410

Answer: assert Solution().minDamage(power = 100, damage = [99, 98, 97, 96, 95], health = [100, 100, 100, 100, 100]) == 1445

Answer: assert Solution().minDamage(power = 15, damage = [3, 7, 11, 19], health = [15, 28, 45, 76]) == 313

Answer: assert Solution().minDamage(power = 300, damage = [50, 100, 150, 200, 250], health = [300, 300, 300, 300, 300]) == 1750

Answer: assert Solution().minDamage(power = 100, damage = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], health = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 2200

Answer: assert Solution().minDamage(power = 33, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34]) == 420

Answer: assert Solution().minDamage(power = 50, damage = [20, 30, 40, 50, 60], health = [100, 150, 200, 250, 300]) == 2450

Answer: assert Solution().minDamage(power = 200, damage = [50, 60, 70, 80, 90, 100], health = [150, 180, 210, 240, 270, 300]) == 2440

Answer: assert Solution().minDamage(power = 1000, damage = [500, 600, 700, 800], health = [900, 1100, 1300, 1500]) == 10600

Answer: assert Solution().minDamage(power = 100, damage = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], health = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 2200

Answer: assert Solution().minDamage(power = 5000, damage = [1000, 2000, 3000, 4000, 5000], health = [2000, 1000, 3000, 4000, 5000]) == 35000

Answer: assert Solution().minDamage(power = 100, damage = [1,2,3,4,5,6,7,8,9,10], health = [100,200,300,400,500,600,700,800,900,1000]) == 1705

Answer: assert Solution().minDamage(power = 100, damage = [200,150,100,50,0], health = [100,100,100,100,100]) == 1000

Answer: assert Solution().minDamage(power = 500, damage = [100, 200, 300, 400, 500], health = [800, 1200, 1600, 2000, 2400]) == 15000

Answer: assert Solution().minDamage(power = 250, damage = [10, 20, 30, 40, 50, 60], health = [500, 600, 700, 800, 900, 1000]) == 2130

Answer: assert Solution().minDamage(power = 5, damage = [1, 3, 2, 4, 5], health = [10, 20, 30, 40, 50]) == 254

Answer: assert Solution().minDamage(power = 2500, damage = [2000, 2500, 3000, 3500], health = [5000, 6000, 7000, 8000]) == 80500

Answer: assert Solution().minDamage(power = 300, damage = [100, 200, 300, 400, 500], health = [150, 300, 450, 600, 750]) == 7700

Answer: assert Solution().minDamage(power = 7, damage = [10, 20, 30, 40, 50, 60], health = [14, 28, 42, 56, 70, 84]) == 5320

Answer: assert Solution().minDamage(power = 1, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) == 220000

Answer: assert Solution().minDamage(power = 1000, damage = [500, 600, 700, 800, 900, 1000], health = [600, 700, 800, 900, 1000, 1100]) == 16500

Answer: assert Solution().minDamage(power = 50, damage = [9, 8, 7, 6, 5, 4, 3, 2, 1], health = [100, 90, 80, 70, 60, 50, 40, 30, 20]) == 303

Answer: assert Solution().minDamage(power = 200, damage = [150, 140, 130, 120, 110], health = [600, 500, 400, 300, 200]) == 3840

Answer: assert Solution().minDamage(power = 5, damage = [2,3,1,4], health = [10,20,30,40]) == 98

Answer: assert Solution().minDamage(power = 100, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]) == 2200

Answer: assert Solution().minDamage(power = 1, damage = [1, 2, 3, 4, 5], health = [10000, 20000, 30000, 40000, 50000]) == 1400000

Answer: assert Solution().minDamage(power = 2000, damage = [500, 500, 500], health = [10000, 10000, 10000]) == 15000

Answer: assert Solution().minDamage(power = 1000, damage = [123,456,789,1011,1213], health = [987,654,321,111,222]) == 8041

Answer: assert Solution().minDamage(power = 1000, damage = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50], health = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) == 2750

Answer: assert Solution().minDamage(power = 25, damage = [12, 18, 22, 27], health = [100, 150, 200, 250]) == 1380

Answer: assert Solution().minDamage(power = 750, damage = [100, 150, 200, 250, 300], health = [1500, 3000, 4500, 6000, 7500]) == 17500

Answer: assert Solution().minDamage(power = 25, damage = [5,15,10,20,25], health = [50,25,75,100,125]) == 570

Answer: assert Solution().minDamage(power = 2500, damage = [1250, 2500, 3750, 5000, 6250], health = [2500, 5000, 7500, 10000, 12500]) == 175000

Answer: assert Solution().minDamage(power = 1, damage = [100,200,300,400,500,600,700,800,900,1000], health = [1,2,3,4,5,6,7,8,9,10]) == 170500

Answer: assert Solution().minDamage(power = 10, damage = [50,40,30,20,10], health = [100,80,60,40,20]) == 2800

Answer: assert Solution().minDamage(power = 10, damage = [100, 100, 100, 100, 100], health = [100, 100, 100, 100, 100]) == 15000

Answer: assert Solution().minDamage(power = 2000, damage = [1500, 500, 1000], health = [3000, 2000, 1500]) == 7500

Answer: assert Solution().minDamage(power = 1000, damage = [500, 500, 500, 500, 500], health = [1000, 1000, 1000, 1000, 1000]) == 7500

Answer: assert Solution().minDamage(power = 100, damage = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100], health = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 21000

Answer: assert Solution().minDamage(power = 1200, damage = [600, 500, 400, 300, 200, 100], health = [2400, 2000, 1600, 1200, 800, 400]) == 9900

Answer: assert Solution().minDamage(power = 1, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 2200

Answer: assert Solution().minDamage(power = 200, damage = [100,100,100,100,100,100,100,100,100,100,100,100,100,100,100], health = [200,200,200,200,200,200,200,200,200,200,200,200,200,200,200]) == 12000

Answer: assert Solution().minDamage(power = 1000, damage = [200, 300, 100], health = [1500, 1000, 500]) == 1300

Answer: assert Solution().minDamage(power = 100, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 210

Answer: assert Solution().minDamage(power = 1000, damage = [1, 10, 100, 1000, 10000], health = [10000, 10000, 10000, 10000, 10000]) == 123450

Answer: assert Solution().minDamage(power = 200, damage = [150, 120, 180, 130, 160], health = [1000, 2000, 3000, 4000, 5000]) == 26450

Answer: assert Solution().minDamage(power = 1, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 715

Answer: assert Solution().minDamage(power = 1, damage = [9999,9998,9997,9996,9995], health = [10000,10000,10000,10000,10000]) == 1499450000

Answer: assert Solution().minDamage(power = 300, damage = [20, 40, 60, 80, 100, 120, 140], health = [900, 1200, 1500, 1800, 2100, 2400, 2700]) == 12600

Answer: assert Solution().minDamage(power = 5, damage = [1, 2, 3, 4, 5], health = [10, 20, 30, 40, 50]) == 280

Answer: assert Solution().minDamage(power = 1, damage = [10000, 10000, 10000], health = [10000, 10000, 10000]) == 600000000

Answer: assert Solution().minDamage(power = 7500, damage = [1500, 2250, 3000, 3750, 4500], health = [7500, 15000, 22500, 30000, 37500]) == 131250

Answer: assert Solution().minDamage(power = 999, damage = [1,2,3,4,5,6,7,8,9,10], health = [10,20,30,40,50,60,70,80,90,100]) == 220

Answer: assert Solution().minDamage(power = 5000, damage = [1000, 2000, 3000, 4000], health = [5000, 5000, 5000, 5000]) == 20000

Answer: assert Solution().minDamage(power = 10, damage = [1,2,3,4,5], health = [100,200,300,400,500]) == 1400

Answer: assert Solution().minDamage(power = 10000, damage = [10000], health = [10000]) == 10000

Answer: assert Solution().minDamage(power = 1000, damage = [999, 998, 997, 996, 995], health = [10000, 20000, 30000, 40000, 50000]) == 348600

Answer: assert Solution().minDamage(power = 300, damage = [150, 150, 150, 150, 150], health = [1500, 1500, 1500, 1500, 1500]) == 11250

Answer: assert Solution().minDamage(power = 2, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 125

Answer: assert Solution().minDamage(power = 30, damage = [15, 20, 25, 30, 35, 40, 45], health = [60, 80, 100, 120, 140, 160, 180]) == 3535

Answer: assert Solution().minDamage(power = 500, damage = [10, 20, 30, 40, 50], health = [50, 100, 150, 200, 250]) == 350

Answer: assert Solution().minDamage(power = 1000, damage = [500, 300, 200, 400], health = [1500, 1200, 1800, 1000]) == 4800

Answer: assert Solution().minDamage(power = 500, damage = [100, 200, 300, 400], health = [1000, 2000, 3000, 4000]) == 13000

Answer: assert Solution().minDamage(power = 2000, damage = [4000,4000,4000,4000,4000], health = [8000,8000,8000,8000,8000]) == 240000

Answer: assert Solution().minDamage(power = 5000, damage = [1000, 2000, 3000, 4000, 5000], health = [1000, 2000, 3000, 4000, 5000]) == 35000

Answer: assert Solution().minDamage(power = 9999, damage = [100, 200, 300, 400, 500], health = [10000, 20000, 30000, 40000, 50000]) == 17500

Answer: assert Solution().minDamage(power = 2500, damage = [1000,2000,3000,4000,5000], health = [5000,4000,3000,2000,1000]) == 45000

Answer: assert Solution().minDamage(power = 3000, damage = [2000,1000,500,1000], health = [1500,1200,2000,2500]) == 9000

Answer: assert Solution().minDamage(power = 100, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 1705

Answer: assert Solution().minDamage(power = 5, damage = [1,1,1,1,1,1,1,1,1,1], health = [10,10,10,10,10,10,10,10,10,10]) == 110

Answer: assert Solution().minDamage(power = 2, damage = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], health = [100,99,98,97,96,95,94,93,92,91,90,89,88,87,86]) == 5468

Answer: assert Solution().minDamage(power = 4000, damage = [100, 200, 300], health = [1000, 2000, 3000]) == 1000

Answer: assert Solution().minDamage(power = 100, damage = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100], health = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5500

Answer: assert Solution().minDamage(power = 700, damage = [100, 200, 300, 400, 500, 600], health = [1500, 2000, 2500, 3000, 3500, 4000]) == 28700

Answer: assert Solution().minDamage(power = 20, damage = [2, 3, 5, 7, 11, 13, 17, 19], health = [40, 60, 100, 140, 220, 260, 340, 380]) == 3478

Answer: assert Solution().minDamage(power = 5, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 1100

Answer: assert Solution().minDamage(power = 8, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], health = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 292

Answer: assert Solution().minDamage(power = 7, damage = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], health = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 2051

Answer: assert Solution().minDamage(power = 500, damage = [200, 300, 400, 500, 600], health = [1000, 1500, 2000, 2500, 3000]) == 24500

Answer: assert Solution().minDamage(power = 100, damage = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], health = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 55

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

from dataclasses import dataclass

@dataclass(frozen=True)
class Enemy:
  damage: int
  timeTakenDown: int

class Solution:
  def minDamage(self, power: int, damage: list[int], health: list[int]) -> int:
    ans = 0
    sumDamage = sum(damage)
    enemies = [Enemy(d, (h + power - 1) // power)
               for d, h in zip(damage, health)]

    # It's better to take down the enemy i first if the damage dealt of taking
    # down i first is less than the damage dealt of taking down j first. So,
    #    damage[i] * t[i] + (t[i] + t[j]) * damage[j] <
    #    damage[j] * t[j] + (t[i] + t[j]) * damage[i]
    # => damage[i] * t[i] + damage[j] * t[i] + damage[j] * t[j] <
    #    damage[j] * t[j] + damage[i] * t[j] + damage[i] * t[i]
    # => damage[j] * t[i] < damage[i] * t[j]
    # => damage[j] / t[j] < damage[i] / t[i]
    enemies.sort(key=lambda x: -x.damage / x.timeTakenDown)

    for enemy in enemies:
      ans += sumDamage * enemy.timeTakenDown
      sumDamage -= enemy.damage

    return ans