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 arrays of integers, fruits and baskets, each of length n, where fruits[i] represents the quantity of the ith type of fruit, and baskets[j] represents the capacity of the jth basket.
From left to right, place the fruits according to these rules:

Each fruit type must be placed in the leftmost available basket with a capacity greater than or equal to the quantity of that fruit type.
Each basket can hold only one type of fruit.
If a fruit type cannot be placed in any basket, it remains unplaced.

Return the number of fruit types that remain unplaced after all possible allocations are made.

Example 1:

Input: fruits = [4,2,5], baskets = [3,5,4]
Output: 1
Explanation:

fruits[0] = 4 is placed in baskets[1] = 5.
fruits[1] = 2 is placed in baskets[0] = 3.
fruits[2] = 5 cannot be placed in baskets[2] = 4.

Since one fruit type remains unplaced, we return 1.

Example 2:

Input: fruits = [3,6,1], baskets = [6,4,7]
Output: 0
Explanation:

fruits[0] = 3 is placed in baskets[0] = 6.
fruits[1] = 6 cannot be placed in baskets[1] = 4 (insufficient capacity) but can be placed in the next available basket, baskets[2] = 7.
fruits[2] = 1 is placed in baskets[1] = 4.

Since all fruits are successfully placed, we return 0.

Constraints:

n == fruits.length == baskets.length
1 <= n <= 105
1 <= fruits[i], baskets[i] <= 109

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

SOLUTION:

Question:
PROBLEM:
You are given two arrays of integers, fruits and baskets, each of length n, where fruits[i] represents the quantity of the ith type of fruit, and baskets[j] represents the capacity of the jth basket.
From left to right, place the fruits according to these rules:

Each fruit type must be placed in the leftmost available basket with a capacity greater than or equal to the quantity of that fruit type.
Each basket can hold only one type of fruit.
If a fruit type cannot be placed in any basket, it remains unplaced.

Return the number of fruit types that remain unplaced after all possible allocations are made.

Example 1:

Input: fruits = [4,2,5], baskets = [3,5,4]
Output: 1
Explanation:

fruits[0] = 4 is placed in baskets[1] = 5.
fruits[1] = 2 is placed in baskets[0] = 3.
fruits[2] = 5 cannot be placed in baskets[2] = 4.

Since one fruit type remains unplaced, we return 1.

Example 2:

Input: fruits = [3,6,1], baskets = [6,4,7]
Output: 0
Explanation:

fruits[0] = 3 is placed in baskets[0] = 6.
fruits[1] = 6 cannot be placed in baskets[1] = 4 (insufficient capacity) but can be placed in the next available basket, baskets[2] = 7.
fruits[2] = 1 is placed in baskets[1] = 4.

Since all fruits are successfully placed, we return 0.

Constraints:

n == fruits.length == baskets.length
1 <= n <= 105
1 <= fruits[i], baskets[i] <= 109

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

SOLUTION:

assert Solution().numOfUnplacedFruits(fruits = [5,5,5,5,5], baskets = [1,2,3,4,5]) == 4

assert Solution().numOfUnplacedFruits(fruits = [4,2,5], baskets = [3,5,4]) == 1

assert Solution().numOfUnplacedFruits(fruits = [1,1,1,1], baskets = [1,1,1,1]) == 0

assert Solution().numOfUnplacedFruits(fruits = [1000000000], baskets = [1000000000]) == 0

assert Solution().numOfUnplacedFruits(fruits = [1,2,3,4], baskets = [4,3,2,1]) == 2

assert Solution().numOfUnplacedFruits(fruits = [1,1,1,1,1], baskets = [1,1,1,1,1]) == 0

assert Solution().numOfUnplacedFruits(fruits = [1,2,3,4], baskets = [10,10,10,10]) == 0

assert Solution().numOfUnplacedFruits(fruits = [10,9,8,7,6], baskets = [6,7,8,9,10]) == 0

assert Solution().numOfUnplacedFruits(fruits = [5,5,5,5], baskets = [5,5,5,5]) == 0

assert Solution().numOfUnplacedFruits(fruits = [1,10,100,1000], baskets = [1000,100,10,1]) == 2

assert Solution().numOfUnplacedFruits(fruits = [7,8,9], baskets = [6,7,8]) == 1

assert Solution().numOfUnplacedFruits(fruits = [10,10,10], baskets = [5,5,5]) == 3

assert Solution().numOfUnplacedFruits(fruits = [1,2,3,4,5], baskets = [5,4,3,2,1]) == 2

assert Solution().numOfUnplacedFruits(fruits = [10,20,30], baskets = [5,15,25]) == 1

assert Solution().numOfUnplacedFruits(fruits = [3,6,1], baskets = [6,4,7]) == 0

assert Solution().numOfUnplacedFruits(fruits = [9, 7, 5, 3, 1], baskets = [1, 3, 5, 7, 9]) == 0

assert Solution().numOfUnplacedFruits(fruits = [5,15,25,35,45], baskets = [10,20,30,40,50]) == 0

assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5], baskets = [5, 5, 5, 5, 5]) == 0

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [50, 40, 30, 20, 10]) == 2

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [20, 30, 40, 50, 60]) == 0

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [25, 35, 15, 45, 55]) == 1

assert Solution().numOfUnplacedFruits(fruits = [1000000000], baskets = [999999999]) == 1

assert Solution().numOfUnplacedFruits(fruits = [7, 3, 8, 2, 9, 5], baskets = [10, 5, 8, 4, 9, 6]) == 0

assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5], baskets = [1, 1, 1, 1, 10]) == 4

assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9, 11, 13], baskets = [13, 11, 9, 7, 5, 3, 1]) == 3

assert Solution().numOfUnplacedFruits(fruits = [10, 10, 10, 10, 10, 10], baskets = [5, 5, 5, 5, 5, 5]) == 6

assert Solution().numOfUnplacedFruits(fruits = [10,20,30,40,50], baskets = [5,15,25,35,45]) == 1

assert Solution().numOfUnplacedFruits(fruits = [50, 40, 30, 20, 10], baskets = [10, 20, 30, 40, 50]) == 0

assert Solution().numOfUnplacedFruits(fruits = [5, 7, 3, 8, 2, 6], baskets = [4, 5, 7, 6, 8, 3]) == 1

assert Solution().numOfUnplacedFruits(fruits = [5, 3, 8, 6, 2], baskets = [4, 7, 8, 5, 1]) == 1

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [5, 25, 15, 40, 30]) == 2

assert Solution().numOfUnplacedFruits(fruits = [1, 1, 1, 1, 10], baskets = [10, 10, 10, 10, 1]) == 1

assert Solution().numOfUnplacedFruits(fruits = [5, 10, 15, 20, 25], baskets = [5, 15, 25, 35, 45, 55]) == 0

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [1, 1, 1, 1, 1]) == 5

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [5, 15, 25, 35, 45]) == 1

assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [100, 100, 100, 100, 1]) == 1

assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5], baskets = [3, 3, 3, 3, 3]) == 5

assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9], baskets = [2, 4, 6, 8, 10]) == 0

assert Solution().numOfUnplacedFruits(fruits = [2, 4, 6, 8, 10], baskets = [1, 3, 5, 7, 9]) == 1

assert Solution().numOfUnplacedFruits(fruits = [9, 11, 13, 15, 17], baskets = [18, 19, 20, 21, 22]) == 0

assert Solution().numOfUnplacedFruits(fruits = [10, 10, 10, 10, 10], baskets = [5, 5, 5, 5, 5]) == 5

assert Solution().numOfUnplacedFruits(fruits = [9, 8, 7, 6, 5], baskets = [10, 9, 8, 7, 6]) == 0

assert Solution().numOfUnplacedFruits(fruits = [2, 3, 1, 5, 4], baskets = [5, 3, 4, 2, 1]) == 2

assert Solution().numOfUnplacedFruits(fruits = [50, 50, 50, 50, 50], baskets = [40, 40, 60, 60, 60]) == 2

assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9, 11], baskets = [2, 4, 6, 8, 10, 12]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [5,5,5,5,5], baskets = [1,2,3,4,5]) == 4

Answer: assert Solution().numOfUnplacedFruits(fruits = [4,2,5], baskets = [3,5,4]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,1,1,1], baskets = [1,1,1,1]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000,1000000000], baskets = [999999999,1000000000]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000], baskets = [1000000000]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,2,3,4], baskets = [4,3,2,1]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,1,1,1,1], baskets = [1,1,1,1,1]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,2,3,4], baskets = [10,10,10,10]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10,9,8,7,6], baskets = [6,7,8,9,10]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [5,5,5,5], baskets = [5,5,5,5]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,10,100,1000], baskets = [1000,100,10,1]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [7,8,9], baskets = [6,7,8]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [10,10,10], baskets = [5,5,5]) == 3

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,2,3,4,5], baskets = [5,4,3,2,1]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [10,20,30], baskets = [5,15,25]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [3,6,1], baskets = [6,4,7]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [9, 7, 5, 3, 1], baskets = [1, 3, 5, 7, 9]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], baskets = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [5,15,25,35,45], baskets = [10,20,30,40,50]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5], baskets = [5, 5, 5, 5, 5]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], baskets = [19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], baskets = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], baskets = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 4

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], baskets = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 0

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

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], baskets = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [50, 40, 30, 20, 10]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [20, 30, 40, 50, 60]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000, 500000000, 250000000, 125000000, 62500000], baskets = [62500000, 125000000, 250000000, 500000000, 1000000000]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], baskets = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], baskets = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [9, 8, 7, 6, 5, 4, 3, 2, 1, 1], baskets = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [100,200,300,400,500,600,700,800,900,1000], baskets = [1000,900,800,700,600,500,400,300,200,100]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [25, 35, 15, 45, 55]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60], baskets = [15, 25, 35, 45, 55, 65]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], baskets = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [10,9,8,7,6,5,4,3,2,1], baskets = [1,2,3,4,5,6,7,8,9,10]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], baskets = [1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == 9

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000, 999999999, 888888888, 777777777, 666666666], baskets = [999999999, 888888888, 777777777, 666666666, 555555555]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000], baskets = [999999999]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,3,5,7,9,11,13,15,17,19], baskets = [2,4,6,8,10,12,14,16,18,20]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], baskets = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512], baskets = [1024, 512, 256, 128, 64, 32, 16, 8, 4, 2]) == 4

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], baskets = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10

Answer: assert Solution().numOfUnplacedFruits(fruits = [7, 3, 8, 2, 9, 5], baskets = [10, 5, 8, 4, 9, 6]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], baskets = [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5], baskets = [1, 1, 1, 1, 10]) == 4

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60], baskets = [60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5]) == 6

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9, 11, 13], baskets = [13, 11, 9, 7, 5, 3, 1]) == 3

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 10, 10, 10, 10, 10], baskets = [5, 5, 5, 5, 5, 5]) == 6

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], baskets = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10,20,30,40,50], baskets = [5,15,25,35,45]) == 1

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

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120], baskets = [120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 6

Answer: assert Solution().numOfUnplacedFruits(fruits = [9, 8, 7, 6, 5, 4, 3, 2, 1], baskets = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [100, 200, 300, 400, 500], baskets = [500, 400, 300, 200, 100]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000], baskets = [10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 1]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50], baskets = [50, 45, 40, 35, 30, 25, 20, 15, 10, 5]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91], baskets = [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [50, 40, 30, 20, 10], baskets = [10, 20, 30, 40, 50]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [999999999, 999999998, 999999997, 999999996, 999999995], baskets = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 7, 3, 8, 2, 6], baskets = [4, 5, 7, 6, 8, 3]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [7,7,7,7,7,7,7,7,7,7], baskets = [5,5,5,5,5,10,10,10,10,10]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4], baskets = [2, 2, 3, 3, 3, 4, 4, 4, 4, 4]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], baskets = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], baskets = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == 4

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 3, 8, 6, 2], baskets = [4, 7, 8, 5, 1]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [5, 25, 15, 40, 30]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], baskets = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], baskets = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 1, 1, 1, 10], baskets = [10, 10, 10, 10, 1]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 10, 15, 20, 25], baskets = [5, 15, 25, 35, 45, 55]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [1, 1, 1, 1, 1]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [5, 15, 25, 35, 45]) == 1

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

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], baskets = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 7

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50, 60], baskets = [60, 50, 40, 30, 20, 10]) == 3

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 20, 30, 40, 50], baskets = [100, 100, 100, 100, 1]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [5, 5, 5, 5, 5], baskets = [3, 3, 3, 3, 3]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [500, 400, 300, 200, 100], baskets = [100, 200, 300, 400, 500]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], baskets = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9], baskets = [2, 4, 6, 8, 10]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [100, 200, 300, 400, 500], baskets = [150, 250, 350, 450, 550]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], baskets = [20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [999999999, 999999998, 999999997, 999999996], baskets = [999999996, 999999997, 999999998, 999999999]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [2, 4, 6, 8, 10], baskets = [1, 3, 5, 7, 9]) == 1

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], baskets = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9

Answer: assert Solution().numOfUnplacedFruits(fruits = [9, 11, 13, 15, 17], baskets = [18, 19, 20, 21, 22]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [10, 10, 10, 10, 10], baskets = [5, 5, 5, 5, 5]) == 5

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000, 1000000000, 1000000000], baskets = [999999999, 999999999, 999999999]) == 3

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512], baskets = [1, 2, 4, 8, 16, 32, 64, 128, 256, 1024]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [9,8,7,6,5,4,3,2,1], baskets = [1,2,3,4,5,6,7,8,10]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [9, 8, 7, 6, 5], baskets = [10, 9, 8, 7, 6]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000, 1000000000, 1000000000], baskets = [999999999, 999999999, 1000000000]) == 2

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

Answer: assert Solution().numOfUnplacedFruits(fruits = [10,10,10,10,10,10,10,10,10,10], baskets = [10,9,8,7,6,5,4,3,2,1]) == 9

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], baskets = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [2, 3, 1, 5, 4], baskets = [5, 3, 4, 2, 1]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [50, 50, 50, 50, 50], baskets = [40, 40, 60, 60, 60]) == 2

Answer: assert Solution().numOfUnplacedFruits(fruits = [1, 3, 5, 7, 9, 11], baskets = [2, 4, 6, 8, 10, 12]) == 0

Answer: assert Solution().numOfUnplacedFruits(fruits = [1000000000, 999999999, 888888888, 777777777, 666666666], baskets = [666666666, 777777777, 888888888, 999999999, 1000000000]) == 0

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)

mn = int(1e10)
class SegmentTree:
    def __init__(self,n):
        # f记录的是特定区间，f[k]，序号为k的点：该节点掌管的索引为l,r，值区间l~r的数字总和
        self.f = [mn for i in range(4*n)]

    def update(self,k,l,r,i,x):
        # 序号为k的索引，掌管的范围是l~r
        if l == r:
            self.f[k] = x
            # 叶子节点
            return
        mid = (l+r)//2
        # 看索引i在左右子树的哪一边。递归更新
        if i <= mid: # 在左子树
            self.update(2*k,l,mid,i,x)
        elif i > mid: # 在右子树
            self.update(2*k+1,mid+1,r,i,x)
        self.f[k] = min(self.f[2*k],self.f[2*k+1])

    def query(self,k,l,r,start,end):
        # start~end始终是l~r的子区间
        # 序号为k的索引，掌管的范围是l~r
        # 在整棵树上进行搜寻 start~end 索引所汇总的范围和
        if l == start and r == end:
            return self.f[k]
        mid = (l+r)//2
        if end <= mid: # 如果start~end完全在左半边，则只需要算左子树
            return self.query(2*k,l,mid,start,end)
        if mid < start: # 如果start~end完全在右半边，则只需要算右子树
            return self.query(2*k+1,mid+1,r,start,end)
        # 否则，需要同时考虑左右孩子
        leftPart = self.query(2*k,l,mid,start,mid) # 注意：在这里最后一个参数是mid而不是end
        rightPart = self.query(2*k+1,mid+1,r,mid+1,end) # 注意：在这里倒数第二个参数是mid+1而不是start
        # 因为：# start~end始终是l~r的子区间，否则递归会没有出口
        return min(leftPart,rightPart)

class Solution:
    def numOfUnplacedFruits(self, fruits: List[int], baskets: List[int]) -> int:
        '''
        离散化 + 线段树
        '''
        n = len(fruits)
        # 离散化
        arr = set(fruits + baskets)
        dt = {}
        arr = sorted(list(arr))
        for i,num in enumerate(arr):
            dt[num] = i

        # init
        tree = SegmentTree(len(arr))
        # 相同 baskets[j] 的值对应的下标队列
        pos = defaultdict(deque)
        for i,num in enumerate(baskets):
            if num not in pos:
                tree.update(1,0,len(arr)-1,dt[num],i)

            pos[num].append(i)

        res = 0
        for num in fruits:
            # 查询[num,∞） 的最小下标，离散化后对应 [ dt[num],len(arr)-1 ]
            j = tree.query(1,0,len(arr)-1,dt[num],len(arr)-1)
            # 找不到对应下标
            if j == mn:
                res += 1
                continue

            tmp = baskets[j]
            pos[tmp].popleft()
            # 若存在，baskets[j] 对应的下一个下标，则单点更新
            if pos[tmp]:
                tree.update(1,0,len(arr)-1,dt[tmp],pos[tmp][0])
            # 若不存在，就更新为一个较大值 mn
            else:
                tree.update(1,0,len(arr)-1,dt[tmp],mn)

        return res


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 array nums of length n and a 2D array queries, where queries[i] = [li, ri, vali].
Each queries[i] represents the following action on nums:

Select a subset of indices in the range [li, ri] from nums.
Decrement the value at each selected index by exactly vali.

A Zero Array is an array with all its elements equal to 0.
Return the minimum possible non-negative value of k, such that after processing the first k queries in sequence, nums becomes a Zero Array. If no such k exists, return -1.

Example 1:

Input: nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]
Output: 2
Explanation:

For query 0 (l = 0, r = 2, val = 1):

Decrement the values at indices [0, 2] by 1.
The array will become [1, 0, 1].

For query 1 (l = 0, r = 2, val = 1):

Decrement the values at indices [0, 2] by 1.
The array will become [0, 0, 0], which is a Zero Array. Therefore, the minimum value of k is 2.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]
Output: -1
Explanation:
It is impossible to make nums a Zero Array even after all the queries.

Example 3:

Input: nums = [1,2,3,2,1], queries = [[0,1,1],[1,2,1],[2,3,2],[3,4,1],[4,4,1]]
Output: 4
Explanation:

For query 0 (l = 0, r = 1, val = 1):

Decrement the values at indices [0, 1] by 1.
The array will become [0, 1, 3, 2, 1].

For query 1 (l = 1, r = 2, val = 1):

Decrement the values at indices [1, 2] by 1.
The array will become [0, 0, 2, 2, 1].

For query 2 (l = 2, r = 3, val = 2):

Decrement the values at indices [2, 3] by 2.
The array will become [0, 0, 0, 0, 1].

For query 3 (l = 3, r = 4, val = 1):

Decrement the value at index 4 by 1.
The array will become [0, 0, 0, 0, 0]. Therefore, the minimum value of k is 4.

Example 4:

Input: nums = [1,2,3,2,6], queries = [[0,1,1],[0,2,1],[1,4,2],[4,4,4],[3,4,1],[4,4,5]]
Output: 4

Constraints:

1 <= nums.length <= 10
0 <= nums[i] <= 1000
1 <= queries.length <= 1000
queries[i] = [li, ri, vali]
0 <= li <= ri < nums.length
1 <= vali <= 10

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

SOLUTION:

Question:
PROBLEM:
You are given an integer array nums of length n and a 2D array queries, where queries[i] = [li, ri, vali].
Each queries[i] represents the following action on nums:

Select a subset of indices in the range [li, ri] from nums.
Decrement the value at each selected index by exactly vali.

A Zero Array is an array with all its elements equal to 0.
Return the minimum possible non-negative value of k, such that after processing the first k queries in sequence, nums becomes a Zero Array. If no such k exists, return -1.

Example 1:

Input: nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]
Output: 2
Explanation:

For query 0 (l = 0, r = 2, val = 1):

Decrement the values at indices [0, 2] by 1.
The array will become [1, 0, 1].

For query 1 (l = 0, r = 2, val = 1):

Decrement the values at indices [0, 2] by 1.
The array will become [0, 0, 0], which is a Zero Array. Therefore, the minimum value of k is 2.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]
Output: -1
Explanation:
It is impossible to make nums a Zero Array even after all the queries.

Example 3:

Input: nums = [1,2,3,2,1], queries = [[0,1,1],[1,2,1],[2,3,2],[3,4,1],[4,4,1]]
Output: 4
Explanation:

For query 0 (l = 0, r = 1, val = 1):

Decrement the values at indices [0, 1] by 1.
The array will become [0, 1, 3, 2, 1].

For query 1 (l = 1, r = 2, val = 1):

Decrement the values at indices [1, 2] by 1.
The array will become [0, 0, 2, 2, 1].

For query 2 (l = 2, r = 3, val = 2):

Decrement the values at indices [2, 3] by 2.
The array will become [0, 0, 0, 0, 1].

For query 3 (l = 3, r = 4, val = 1):

Decrement the value at index 4 by 1.
The array will become [0, 0, 0, 0, 0]. Therefore, the minimum value of k is 4.

Example 4:

Input: nums = [1,2,3,2,6], queries = [[0,1,1],[0,2,1],[1,4,2],[4,4,4],[3,4,1],[4,4,5]]
Output: 4

Constraints:

1 <= nums.length <= 10
0 <= nums[i] <= 1000
1 <= queries.length <= 1000
queries[i] = [li, ri, vali]
0 <= li <= ri < nums.length
1 <= vali <= 10

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

SOLUTION:

Answer: assert Solution().minZeroArray(nums = [1,2,3,2,6], queries = [[0,1,1],[0,2,1],[1,4,2],[4,4,4],[3,4,1],[4,4,5]]) == 4

Answer: assert Solution().minZeroArray(nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]) == 2

Answer: assert Solution().minZeroArray(nums = [1,2,3,2,1], queries = [[0,1,1],[1,2,1],[2,3,2],[3,4,1],[4,4,1]]) == 4

Answer: assert Solution().minZeroArray(nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,9,1],[0,9,2],[0,9,3],[0,9,4],[0,9,5],[0,9,6],[0,9,7],[0,9,8],[0,9,9],[0,9,10]]) == 4

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [2,4,6,8,10,8,6,4,2,0], queries = [[0,4,2],[1,5,3],[2,6,4],[3,7,5],[4,8,6]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,4,1],[2,6,2],[1,7,3],[0,9,4],[3,5,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [[0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == 1

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50,60,70,80,90,100], queries = [[0,4,10],[5,9,10],[0,9,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [3,6,9,12,15], queries = [[0,0,3],[1,1,6],[2,2,9],[3,3,12],[4,4,15]]) == 5

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,0,1],[1,1,1],[2,2,1],[3,3,1],[4,4,1],[5,5,1],[6,6,1],[7,7,1],[8,8,1],[9,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,6,7,8,9,10,11,12,13,14], queries = [[0,9,1],[1,8,2],[2,7,3],[3,6,4],[4,5,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], queries = [[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == 2

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,2,3],[3,5,3],[6,8,3],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 6

Answer: assert Solution().minZeroArray(nums = [8,7,6,5,4,3,2,1,0,1], queries = [[0,9,1],[0,4,2],[5,9,2],[0,9,3],[0,9,4]]) == 5

Answer: assert Solution().minZeroArray(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [[0,0,1],[1,1,1],[2,2,1],[3,3,1],[4,4,1],[5,5,1],[6,6,1],[7,7,1],[8,8,1],[9,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100], queries = [[0,4,20],[5,9,20],[0,9,20],[0,9,20],[0,9,20],[0,9,20],[0,9,20],[0,9,20],[0,9,20],[0,9,20]]) == 6

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50], queries = [[0,2,5],[1,3,10],[2,4,15],[0,4,20]]) == -1

Answer: assert Solution().minZeroArray(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], queries = [[0, 9, 1], [0, 4, 2], [5, 9, 3], [0, 2, 1], [7, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == 10

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,0,10],[1,1,10],[2,2,10],[3,3,10],[4,4,10],[5,5,10],[6,6,10],[7,7,10],[8,8,10],[9,9,10]]) == -1

Answer: assert Solution().minZeroArray(nums = [9,8,7,6,5,4,3,2,1,0], queries = [[0,9,1],[0,8,2],[0,7,3],[0,6,4],[0,5,5]]) == 4

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], queries = [[0,4,100],[5,9,200],[0,9,300],[0,9,100],[0,9,50]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[0,9,2],[0,9,3],[0,9,4],[0,9,5],[0,9,6],[0,9,7],[0,9,8],[0,9,9],[0,9,10]]) == 4

Answer: assert Solution().minZeroArray(nums = [1,3,5,7,9,11,13,15,17,19], queries = [[0,0,1],[1,1,3],[2,2,5],[3,3,7],[4,4,9],[5,5,11],[6,6,13],[7,7,15],[8,8,17],[9,9,19]]) == 10

Answer: assert Solution().minZeroArray(nums = [10,20,30,40,50,60,70,80,90,100], queries = [[0,4,5],[5,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5],[0,9,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], queries = [[0, 9, 1], [1, 8, 1], [2, 7, 1], [3, 6, 1], [4, 5, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [2,2,2,2,2,2,2,2,2,2], queries = [[0,4,1],[5,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 3

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,0,1],[1,1,1],[2,2,1],[3,3,1],[4,4,1],[5,5,1],[6,6,1],[7,7,1],[8,8,1],[9,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], queries = [[0,1,1],[2,3,2],[4,5,3],[6,7,4],[8,9,5],[0,9,1],[2,7,2],[1,8,3],[3,6,4],[4,5,5]]) == 5

Answer: assert Solution().minZeroArray(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], queries = [[0, 9, 1], [0, 4, 2], [5, 9, 3], [0, 2, 1], [7, 9, 1], [0, 9, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [2,4,6,8,10,12,14,16,18,20], queries = [[0,1,2],[1,2,2],[2,3,2],[3,4,2],[4,5,2],[5,6,2],[6,7,2],[7,8,2],[8,9,2],[9,9,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], queries = [[0, 4, 1], [1, 5, 1], [2, 6, 1], [3, 7, 1], [4, 8, 1], [5, 9, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4,1],[5,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 6

Answer: assert Solution().minZeroArray(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], queries = [[0,4,5],[0,4,10],[0,4,15],[0,4,20],[0,4,25],[5,9,30],[5,9,35],[5,9,40],[5,9,45],[5,9,50]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10]]) == -1

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 3

Answer: assert Solution().minZeroArray(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], queries = [[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3],[0,9,3]]) == 10

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,1],[0,8,1],[0,7,1],[0,6,1],[0,5,1],[0,4,1],[0,3,1],[0,2,1],[0,1,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,3,5,7,9,11,13,15,17,19], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1],[5,4,1],[6,3,1],[7,2,1],[8,1,1],[9,0,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [2,4,6,8,10,12,14,16,18,20], queries = [[0,4,2],[0,4,2],[0,4,2],[5,9,2],[5,9,2],[5,9,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1],[5,4,1],[6,3,1],[7,2,1],[8,1,1],[9,0,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1],[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 5

Answer: assert Solution().minZeroArray(nums = [20,20,20,20,20,20,20,20,20,20], queries = [[0,9,2],[1,8,2],[2,7,2],[3,6,2],[4,5,2],[5,4,2],[6,3,2],[7,2,2],[8,1,2],[9,0,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,1,2],[1,2,2],[2,3,2],[3,4,2],[4,5,2],[5,6,2],[6,7,2],[7,8,2],[8,9,2],[9,9,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [10, 20, 30, 40, 50], queries = [[0, 0, 10], [1, 1, 10], [2, 2, 10], [3, 3, 10], [4, 4, 10], [0, 4, 5]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,8,1],[1,8,1],[1,7,1],[2,7,1],[2,6,1],[3,6,1],[3,5,1],[4,5,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], queries = [[0, 9, 2], [1, 8, 2], [2, 7, 2], [3, 6, 2], [4, 5, 2], [0, 9, 1], [0, 9, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10]]) == -1

Answer: assert Solution().minZeroArray(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], queries = [[0,4,1],[5,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 6

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3,3,3,3,3], queries = [[0,2,1],[3,5,1],[6,8,1],[0,9,3]]) == 4

Answer: assert Solution().minZeroArray(nums = [9,8,7,6,5,4,3,2,1,0], queries = [[0,0,9],[1,1,8],[2,2,7],[3,3,6],[4,4,5],[5,5,4],[6,6,3],[7,7,2],[8,8,1],[9,9,0]]) == 9

Answer: assert Solution().minZeroArray(nums = [10,10,10,10,10,10,10,10,10,10], queries = [[0,9,1],[0,4,1],[5,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [7,6,5,4,3,2,1], queries = [[0,3,2],[1,2,1],[2,5,3],[0,6,1],[1,4,4]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,10],[1,8,8],[2,7,6],[3,6,4],[4,5,2],[0,9,10],[1,8,8],[2,7,6],[3,6,4],[4,5,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [9,8,7,6,5,4,3,2,1,0], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1],[5,4,1],[6,3,1],[7,2,1],[8,1,1],[9,0,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [7,7,7,7,7,7,7], queries = [[0,6,1],[1,5,2],[2,4,3],[3,3,4]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,4,1],[1,5,2],[2,6,3],[3,7,4],[4,8,5],[5,9,6]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,1],[0,4,1],[5,9,1],[2,7,1],[3,6,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,2,3],[1,3,3],[2,4,3],[3,5,3],[4,6,3],[5,7,3],[6,8,3],[7,9,3],[8,9,3],[9,9,3]]) == -1

Answer: assert Solution().minZeroArray(nums = [5, 5, 5, 5, 5], queries = [[0, 4, 2], [0, 4, 2], [0, 4, 2], [0, 4, 2], [0, 4, 2]]) == -1

Answer: assert Solution().minZeroArray(nums = [10, 20, 30, 40, 50], queries = [[0,4,5],[1,3,10],[2,2,20],[3,4,15]]) == -1

Answer: assert Solution().minZeroArray(nums = [100,200,300,400,500,600,700,800,900,1000], queries = [[0,9,100],[0,9,100],[0,9,100],[0,9,100],[0,9,100],[0,9,100],[0,9,100],[0,9,100],[0,9,100],[0,9,100]]) == 10

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[0,8,1],[0,7,1],[0,6,1],[0,5,1],[0,4,1],[0,3,1],[0,2,1],[0,1,1],[0,0,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [[0, 4, 1], [5, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == 2

Answer: assert Solution().minZeroArray(nums = [100, 100, 100, 100, 100], queries = [[0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10], [0, 4, 10]]) == 10

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,1,1],[1,2,1],[2,3,1],[3,4,1],[4,5,1],[5,6,1],[6,7,1],[7,8,1],[8,9,1],[9,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [10,10,10,10,10,10,10,10,10,10], queries = [[0,9,3],[0,9,2],[0,9,1],[0,9,1],[0,9,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,9,1],[1,8,2],[2,7,3],[3,6,4],[4,5,5],[0,4,6],[5,9,7]]) == -1

Answer: assert Solution().minZeroArray(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], queries = [[0, 9, 1], [1, 8, 1], [2, 7, 1], [3, 6, 1], [4, 5, 1]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1,0,1,2,3,4], queries = [[0,9,1],[0,4,2],[5,9,3],[2,7,1],[3,6,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [7,7,7,7,7,7,7], queries = [[0,6,1],[1,5,2],[2,4,3],[3,6,4],[0,3,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], queries = [[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,1,1,1,1,1,1,1,1,1], queries = [[0,9,1],[0,8,1],[0,7,1],[0,6,1],[0,5,1],[0,4,1],[0,3,1],[0,2,1],[0,1,1],[0,0,1]]) == 1

Answer: assert Solution().minZeroArray(nums = [10,9,8,7,6,5,4,3,2,1], queries = [[0,9,1],[1,8,1],[2,7,1],[3,6,1],[4,5,1],[5,4,1],[6,3,1],[7,2,1],[8,1,1],[9,0,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [100, 0, 100, 0, 100], queries = [[0, 4, 50], [1, 3, 25], [0, 4, 25], [0, 4, 25], [0, 4, 1]]) == 4

Answer: assert Solution().minZeroArray(nums = [9,8,7,6,5,4,3,2,1,0], queries = [[0,1,2],[1,2,2],[2,3,2],[3,4,2],[4,5,2],[5,6,2],[6,7,2],[7,8,2],[8,9,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], queries = [[0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == 0

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1,0,1,2,3,4], queries = [[0,2,1],[1,3,2],[2,4,3],[3,5,4],[4,6,5],[5,7,6],[6,8,7],[7,9,8]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5], queries = [[0,4,1],[1,3,2],[2,2,3],[0,4,1]]) == -1

Answer: assert Solution().minZeroArray(nums = [6,6,6,6,6,6,6,6,6,6], queries = [[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 6

Answer: assert Solution().minZeroArray(nums = [15,10,5,10,15], queries = [[0,4,5],[1,3,3],[2,2,2],[0,4,4]]) == -1

Answer: assert Solution().minZeroArray(nums = [1,2,3,4,5,6,7,8,9,10], queries = [[0,4,2],[5,9,2],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1],[0,9,1]]) == 10

Answer: assert Solution().minZeroArray(nums = [3,3,3,3,3,3], queries = [[0,5,1],[1,4,1],[2,3,1],[0,2,2],[3,5,2]]) == 5

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5,5,5,5,5,5], queries = [[0,4,1],[5,9,1],[0,9,1],[0,4,1],[5,9,1],[0,9,1],[0,4,1],[5,9,1],[0,9,1],[0,4,1]]) == 8

Answer: assert Solution().minZeroArray(nums = [1,3,5,7,9,11,13,15,17,19], queries = [[0,9,2],[1,8,2],[2,7,2],[3,6,2],[4,5,2]]) == -1

Answer: assert Solution().minZeroArray(nums = [20,18,16,14,12,10,8,6,4,2], queries = [[0,2,3],[1,3,3],[2,4,3],[3,5,3],[4,6,3],[5,7,3],[6,8,3],[7,9,3],[8,9,3]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,4,3,2,1], queries = [[0,4,1],[0,3,2],[1,2,3],[2,4,4],[3,4,5]]) == -1

Answer: assert Solution().minZeroArray(nums = [5,5,5,5,5], queries = [[0,0,5],[1,1,5],[2,2,5],[3,3,5],[4,4,5],[0,4,5]]) == 5

Answer: assert Solution().minZeroArray(nums = [1, 3, 5, 7, 9, 7, 5, 3, 1], queries = [[0, 8, 1], [1, 7, 2], [2, 6, 3], [3, 5, 4], [4, 4, 5], [0, 8, 1]]) == 4

Answer: assert Solution().minZeroArray(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], queries = [[0, 9, 10], [1, 8, 20], [2, 7, 30], [3, 6, 40], [4, 5, 50], [0, 9, 10]]) == -1

Answer: assert Solution().minZeroArray(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], queries = [[0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2], [0, 9, 2]]) == 10

Answer: assert Solution().minZeroArray(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], queries = [[0, 4, 2], [5, 9, 2], [2, 7, 2], [0, 9, 1], [0, 9, 1], [0, 9, 1]]) == 6

Answer: assert Solution().minZeroArray(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], queries = [[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10],[0,9,10]]) == -1

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 minZeroArray(self, nums: list[int], queries: list[list[int]]) -> int:
    if all(num == 0 for num in nums):
      return 0

    n = len(nums)
    subsetSums = [{0} for _ in range(n)]

    for k, (l, r, val) in enumerate(queries):
      for i in range(l, r + 1):
        newSums = {subsetSum + val for subsetSum in subsetSums[i]}
        subsetSums[i].update(newSums)
      if all(nums[i] in subsetSums[i] for i in range(n)):
        return k + 1

    return -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:
You are given a 2D integer array properties having dimensions n x m and an integer k.
Define a function intersect(a, b) that returns the number of distinct integers common to both arrays a and b.
Construct an undirected graph where each index i corresponds to properties[i]. There is an edge between node i and node j if and only if intersect(properties[i], properties[j]) >= k, where i and j are in the range [0, n - 1] and i != j.
Return the number of connected components in the resulting graph.

Example 1:

Input: properties = [[1,2],[1,1],[3,4],[4,5],[5,6],[7,7]], k = 1
Output: 3
Explanation:
The graph formed has 3 connected components:

Example 2:

Input: properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2
Output: 1
Explanation:
The graph formed has 1 connected component:

Example 3:

Input: properties = [[1,1],[1,1]], k = 2
Output: 2
Explanation:
intersect(properties[0], properties[1]) = 1, which is less than k. This means there is no edge between properties[0] and properties[1] in the graph.

Constraints:

1 <= n == properties.length <= 100
1 <= m == properties[i].length <= 100
1 <= properties[i][j] <= 100
1 <= k <= m

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

SOLUTION:

Question:
PROBLEM:
You are given a 2D integer array properties having dimensions n x m and an integer k.
Define a function intersect(a, b) that returns the number of distinct integers common to both arrays a and b.
Construct an undirected graph where each index i corresponds to properties[i]. There is an edge between node i and node j if and only if intersect(properties[i], properties[j]) >= k, where i and j are in the range [0, n - 1] and i != j.
Return the number of connected components in the resulting graph.

Example 1:

Input: properties = [[1,2],[1,1],[3,4],[4,5],[5,6],[7,7]], k = 1
Output: 3
Explanation:
The graph formed has 3 connected components:

Example 2:

Input: properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2
Output: 1
Explanation:
The graph formed has 1 connected component:

Example 3:

Input: properties = [[1,1],[1,1]], k = 2
Output: 2
Explanation:
intersect(properties[0], properties[1]) = 1, which is less than k. This means there is no edge between properties[0] and properties[1] in the graph.

Constraints:

1 <= n == properties.length <= 100
1 <= m == properties[i].length <= 100
1 <= properties[i][j] <= 100
1 <= k <= m

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

SOLUTION:

assert Solution().numberOfComponents(properties = [[1,1,1],[1,1,1],[1,1,1]], k = 1) == 1

assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,6]], k = 1) == 1

assert Solution().numberOfComponents(properties = [[1,1,1,1],[1,1,1,1],[1,1,1,1]], k = 4) == 3

assert Solution().numberOfComponents(properties = [[1,1],[1,1]], k = 2) == 2

assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5]], k = 1) == 1

assert Solution().numberOfComponents(properties = [[1],[2],[3],[4],[5]], k = 1) == 5

assert Solution().numberOfComponents(properties = [[1,2],[3,4],[5,6],[7,8]], k = 0) == 1

assert Solution().numberOfComponents(properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2) == 1

assert Solution().numberOfComponents(properties = [[1,2,3],[4,5,6],[7,8,9]], k = 2) == 3

assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,1]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,7]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[10,20,30],[30,40,50],[40,50,60],[50,60,70]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1]], k = 4) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,1,1],[1,1,1],[1,1,1]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,6]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[1,1,1,1],[1,1,1,1]], k = 4) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,1],[1,1]], k = 2) == 2

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[2,3,4],[3,4,5],[4,5,6]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[4,5,6],[7,8,9],[1,4,7],[2,5,8],[3,6,9]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[10,20,30],[20,30,40],[30,40,50],[40,50,60]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2],[1,1],[3,4],[4,5],[5,6],[7,7]], k = 1) == 3

Answer: assert Solution().numberOfComponents(properties = [[1],[2],[3],[4],[5]], k = 1) == 5

Answer: assert Solution().numberOfComponents(properties = [[1,2],[3,4],[5,6],[7,8]], k = 0) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[10,20,30],[10,20,30],[10,20,30],[10,20,30]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[4,5,6],[7,8,9]], k = 2) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20],[1,11,21,31,41,51,61,71,81,91]], k = 2) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9],[2,3,4,5,6,7,8,9,10],[3,4,5,6,7,8,9,10,11]], k = 4) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,9,10,11],[3,4,5,6,7,8,9,10,11,12],[10,11,12,13,14,15,16,17,18,19]], k = 4) == 2

Answer: assert Solution().numberOfComponents(properties = [[5,5,5],[5,5,5],[5,5,5],[5,5,5],[5,5,5],[5,5,5]], k = 3) == 6

Answer: assert Solution().numberOfComponents(properties = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [2, 3, 4, 5, 6], [6, 5, 4, 3, 2], [3, 4, 5, 6, 7]], k = 4) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,11],[1,2,3,4,5,6,7,8,9,12]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[1,1,1,2],[1,1,2,2],[1,2,2,2]], k = 3) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]], k = 10) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[1,3,5,7,9,11,13,15,17,19],[2,4,6,8,10,12,14,16,18,20],[1,4,7,10,13,16,19,22,25,28]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[2,3,4],[4,3,5],[5,6,7],[7,8,9]], k = 2) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6],[6,7,8,9,10,11],[11,12,13,14,15,16],[16,17,18,19,20,21]], k = 3) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,11],[1,2,3,4,5,6,7,8,9,12],[1,2,3,4,5,6,7,8,9,13]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[10,20,30,40,50],[50,40,30,20,10],[1,2,3,4,5],[5,4,3,2,1],[10,15,20,25,30]], k = 2) == 2

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[5,10,15,20],[10,15,20,25],[15,20,25,30],[20,25,30,35],[25,30,35,40]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[2,2,2,2],[1,1,2,2],[2,2,1,1],[1,2,1,2],[2,1,2,1]], k = 2) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1,1],[2,2,2,2,2],[3,3,3,3,3],[1,2,3,4,5],[2,3,4,5,6]], k = 3) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,1]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1, 2], [2, 3], [3, 4], [4, 1], [1, 3], [2, 4], [1, 4], [2, 3]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,1]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1, 10, 100], [10, 100, 1000], [100, 1000, 10000], [1000, 10000, 100000], [100000, 1, 10]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5],[2,3,4,5,6],[3,4,5,6,7],[4,5,6,7,8],[5,6,7,8,9]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[2,3,4],[4,5,6],[6,7,8],[8,9,10],[10,11,12]], k = 2) == 5

Answer: assert Solution().numberOfComponents(properties = [[10,20,30],[20,30,40],[30,40,50],[40,50,60],[50,60,70]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1],[1,1,2],[1,2,2],[2,2,2],[2,2,3],[2,3,3],[3,3,3]], k = 2) == 5

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20],[21,22,23,24,25,26,27,28,29,30]], k = 1) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,9,10,11],[3,4,5,6,7,8,9,10,11,12]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,2,2,3,3,4,4,5,5],[1,2,2,3,3,4,4,5,5,6],[1,1,2,3,3,4,4,5,6,6],[1,2,2,3,3,4,4,5,6,7],[1,2,2,3,3,4,4,5,6,8]], k = 4) == 1

Answer: assert Solution().numberOfComponents(properties = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [1, 4, 7], [2, 5, 8], [3, 6, 9]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]], k = 15) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20],[21,22,23,24,25,26,27,28,29,30]], k = 5) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]], k = 10) == 1

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

Answer: assert Solution().numberOfComponents(properties = [[10,20,30,40,50],[10,20,30,60,70],[10,20,50,60,70],[10,50,60,70,80]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,2,3,4,5,6,7,8,9,10],[3,3,3,4,5,6,7,8,9,10]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[2,3,4],[3,4,5],[4,5,6],[5,6,7],[6,7,8],[7,8,9],[8,9,10]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[2,2,2,2],[3,3,3,3],[1,2,3,4],[4,5,6,7]], k = 2) == 5

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39]], k = 6) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], [1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15], [4, 8, 12, 16]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]], k = 6) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20],[21,22,23,24,25,26,27,28,29,30],[31,32,33,34,35,36,37,38,39,40]], k = 1) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,1,2,2],[2,2,3,3],[3,3,4,4],[4,4,1,1]], k = 2) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,1],[1,3],[3,5]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5],[2,3,4,5,6],[3,4,5,6,7],[4,5,6,7,8]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,9,10,1],[3,4,5,6,7,8,9,10,1,2],[4,5,6,7,8,9,10,1,2,3]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1,1,1,1,1,1,1],[2,2,2,2,2,2,2,2,2,2],[3,3,3,3,3,3,3,3,3,3],[1,2,3,4,5,6,7,8,9,10]], k = 5) == 4

Answer: assert Solution().numberOfComponents(properties = [[1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3], [1, 2, 3]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[10,20,30],[10,20,40],[10,30,40],[20,30,40],[10,20,30,40]], k = 2) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,4,6,8,10,12,14,16,18,20],[3,6,9,12,15,18,21,24,27,30],[4,8,12,16,20,24,28,32,36,40]], k = 4) == 2

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[2,2,2,2],[3,3,3,3],[1,2,3,4]], k = 2) == 4

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

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1,1,1,1,1,1,1],[2,2,2,2,2,2,2,2,2,2],[3,3,3,3,3,3,3,3,3,3],[4,4,4,4,4,4,4,4,4,4]], k = 5) == 4

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,1,2,2],[2,2,3,3],[3,3,4,4],[4,4,5,5],[5,5,6,6]], k = 2) == 5

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1,1],[2,2,2,2,2],[3,3,3,3,3],[4,4,4,4,4],[5,5,5,5,5]], k = 1) == 5

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10]], k = 8) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6],[2,3,4,5,6,7],[3,4,5,6,7,8],[4,5,6,7,8,9]], k = 4) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2],[2,3],[3,4],[4,5],[5,1],[1,3],[2,4],[3,5],[4,1],[5,2]], k = 1) == 1

Answer: assert Solution().numberOfComponents(properties = [[10,20,30],[10,20,40],[10,30,50],[20,30,60],[30,40,50]], k = 2) == 1

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

Answer: assert Solution().numberOfComponents(properties = [[1,2,2,3,4,4,5],[2,3,3,4,4,5,5],[3,4,4,5,5,6,6],[4,5,5,6,6,7,7],[5,6,6,7,7,8,8]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6],[2,3,4,5,6,7],[3,4,5,6,7,8],[4,5,6,7,8,9],[5,6,7,8,9,10]], k = 4) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5],[6,7,8,9,10],[1,6,2,7,3],[8,4,9,5,10],[11,12,13,14,15]], k = 2) == 2

Answer: assert Solution().numberOfComponents(properties = [[1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 2, 2], [1, 2, 2, 2], [2, 2, 2, 2]], k = 3) == 5

Answer: assert Solution().numberOfComponents(properties = [[1,1,1,1],[1,1,1,2],[1,1,2,2],[1,2,2,2],[2,2,2,2]], k = 3) == 5

Answer: assert Solution().numberOfComponents(properties = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5],[5,4,3,2,1],[1,2,3,4,5],[5,4,3,2,1],[1,2,3,4,5]], k = 3) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,9,10,11],[3,4,5,6,7,8,9,10,11,12]], k = 4) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5],[5,6,7,8,9],[9,10,11,12,13],[13,14,15,16,17],[17,18,19,20,21],[21,22,23,24,25]], k = 2) == 6

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[10,9,8,7,6,5,4,3,2,1],[1,3,5,7,9,11,13,15,17,19]], k = 5) == 1

Answer: assert Solution().numberOfComponents(properties = [[1,2,3],[4,5,6],[7,8,9],[10,11,12],[13,14,15],[1,4,7],[2,5,8],[3,6,9]], k = 1) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,1,1],[1,1,2],[1,2,2],[2,2,2],[2,2,1]], k = 2) == 3

Answer: assert Solution().numberOfComponents(properties = [[1,1],[2,2],[3,3],[4,4],[5,5],[6,6],[7,7],[8,8],[9,9],[10,10]], k = 1) == 10

Answer: assert Solution().numberOfComponents(properties = [[1,2,3,4,5,6,7,8,9,10],[2,3,4,5,6,7,8,9,10,1],[3,4,5,6,7,8,9,10,1,2]], k = 4) == 1

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 numberOfComponents(self, properties: List[List[int]], k: int) -> int:
        def dfs(i: int) -> None:
            vis[i] = True
            for j in g[i]:
                if not vis[j]:
                    dfs(j)

        n = len(properties)
        ss = list(map(set, properties))
        g = [[] for _ in range(n)]
        for i, s1 in enumerate(ss):
            for j in range(i):
                s2 = ss[j]
                if len(s1 & s2) >= k:
                    g[i].append(j)
                    g[j].append(i)
        ans = 0
        vis = [False] * n
        for i in range(n):
            if not vis[i]:
                dfs(i)
                ans += 1
        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 two integer arrays, skill and mana, of length n and m, respectively.
In a laboratory, n wizards must brew m potions in order. Each potion has a mana capacity mana[j] and must pass through all the wizards sequentially to be brewed properly. The time taken by the ith wizard on the jth potion is timeij = skill[i] * mana[j].
Since the brewing process is delicate, a potion must be passed to the next wizard immediately after the current wizard completes their work. This means the timing must be synchronized so that each wizard begins working on a potion exactly when it arrives.
Return the minimum amount of time required for the potions to be brewed properly.

Example 1:

Input: skill = [1,5,2,4], mana = [5,1,4,2]
Output: 110
Explanation:

Potion Number
Start time
Wizard 0 done by
Wizard 1 done by
Wizard 2 done by
Wizard 3 done by

0
0
5
30
40
60

1
52
53
58
60
64

2
54
58
78
86
102

3
86
88
98
102
110

As an example for why wizard 0 cannot start working on the 1st potion before time t = 52, consider the case where the wizards started preparing the 1st potion at time t = 50. At time t = 58, wizard 2 is done with the 1st potion, but wizard 3 will still be working on the 0th potion till time t = 60.

Example 2:

Input: skill = [1,1,1], mana = [1,1,1]
Output: 5
Explanation:

Preparation of the 0th potion begins at time t = 0, and is completed by time t = 3.
Preparation of the 1st potion begins at time t = 1, and is completed by time t = 4.
Preparation of the 2nd potion begins at time t = 2, and is completed by time t = 5.

Example 3:

Input: skill = [1,2,3,4], mana = [1,2]
Output: 21

Constraints:

n == skill.length
m == mana.length
1 <= n, m <= 5000
1 <= mana[i], skill[i] <= 5000

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

SOLUTION:

Question:
PROBLEM:
You are given two integer arrays, skill and mana, of length n and m, respectively.
In a laboratory, n wizards must brew m potions in order. Each potion has a mana capacity mana[j] and must pass through all the wizards sequentially to be brewed properly. The time taken by the ith wizard on the jth potion is timeij = skill[i] * mana[j].
Since the brewing process is delicate, a potion must be passed to the next wizard immediately after the current wizard completes their work. This means the timing must be synchronized so that each wizard begins working on a potion exactly when it arrives.
Return the minimum amount of time required for the potions to be brewed properly.

Example 1:

Input: skill = [1,5,2,4], mana = [5,1,4,2]
Output: 110
Explanation:

Potion Number
Start time
Wizard 0 done by
Wizard 1 done by
Wizard 2 done by
Wizard 3 done by

0
0
5
30
40
60

1
52
53
58
60
64

2
54
58
78
86
102

3
86
88
98
102
110

As an example for why wizard 0 cannot start working on the 1st potion before time t = 52, consider the case where the wizards started preparing the 1st potion at time t = 50. At time t = 58, wizard 2 is done with the 1st potion, but wizard 3 will still be working on the 0th potion till time t = 60.

Example 2:

Input: skill = [1,1,1], mana = [1,1,1]
Output: 5
Explanation:

Preparation of the 0th potion begins at time t = 0, and is completed by time t = 3.
Preparation of the 1st potion begins at time t = 1, and is completed by time t = 4.
Preparation of the 2nd potion begins at time t = 2, and is completed by time t = 5.

Example 3:

Input: skill = [1,2,3,4], mana = [1,2]
Output: 21

Constraints:

n == skill.length
m == mana.length
1 <= n, m <= 5000
1 <= mana[i], skill[i] <= 5000

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

SOLUTION:

assert Solution().minTime(skill = [3,2,1], mana = [6,5,4]) == 57

assert Solution().minTime(skill = [1,1,1], mana = [1,1,1]) == 5

assert Solution().minTime(skill = [1,2,3], mana = [4,5,6,7]) == 78

assert Solution().minTime(skill = [1,2,3,4], mana = [1,2]) == 21

assert Solution().minTime(skill = [1, 3, 2, 4], mana = [2, 3, 4, 5]) == 74

Answer: assert Solution().minTime(skill = [10,20,30], mana = [1,2,3,4,5]) == 490

Answer: assert Solution().minTime(skill = [3,2,1], mana = [6,5,4]) == 57

Answer: assert Solution().minTime(skill = [1,1,1], mana = [1,1,1]) == 5

Answer: assert Solution().minTime(skill = [1,2,3], mana = [4,5,6,7]) == 78

Answer: assert Solution().minTime(skill = [5000, 5000], mana = [1, 5000]) == 50005000

Answer: assert Solution().minTime(skill = [1, 2, 3], mana = [4, 5, 6, 7, 8]) == 102

Answer: assert Solution().minTime(skill = [1,5,2,4], mana = [5,1,4,2]) == 110

Answer: assert Solution().minTime(skill = [10, 20, 30], mana = [1, 2, 3, 4, 5]) == 490

Answer: assert Solution().minTime(skill = [1,2,3,4], mana = [1,2]) == 21

Answer: assert Solution().minTime(skill = [5000, 5000, 5000], mana = [5000, 5000, 5000]) == 125000000

Answer: assert Solution().minTime(skill = [3, 1, 4, 1, 5], mana = [9, 2, 6, 5, 3, 5]) == 275

Answer: assert Solution().minTime(skill = [2, 3, 4, 5], mana = [1, 2, 3, 4, 5, 6, 7]) == 159

Answer: assert Solution().minTime(skill = [1, 1, 2, 2, 3, 3], mana = [1, 2, 3, 4, 5, 6]) == 94

Answer: assert Solution().minTime(skill = [10, 20, 30, 40, 50], mana = [5, 10, 15, 20, 25]) == 4750

Answer: assert Solution().minTime(skill = [2, 3, 5, 7, 11, 13, 17, 19], mana = [23, 29, 31, 37, 41, 43, 47, 53, 59, 61]) == 9500

Answer: assert Solution().minTime(skill = [2, 3, 5, 7, 11], mana = [13, 17, 19, 23, 29, 31, 37, 41]) == 2531

Answer: assert Solution().minTime(skill = [100, 100, 100, 100, 100], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9500

Answer: assert Solution().minTime(skill = [5, 5, 5, 5, 5], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 475

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], mana = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 3375

Answer: assert Solution().minTime(skill = [4999, 4998, 4997, 4996], mana = [5000, 4999, 4998, 4997, 4996]) == 199820050

Answer: assert Solution().minTime(skill = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], mana = [10, 20, 30, 40, 50]) == 29500

Answer: assert Solution().minTime(skill = [100, 200, 300, 400, 500], mana = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 295000

Answer: assert Solution().minTime(skill = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29], mana = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 4585

Answer: assert Solution().minTime(skill = [300, 200, 100, 400, 500], mana = [100, 200, 300, 400, 500]) == 1050000

Answer: assert Solution().minTime(skill = [1,2,3,4,5,6], mana = [6,5,4,3,2,1]) == 216

Answer: assert Solution().minTime(skill = [4,3,2,1], mana = [100,200,300,400,500]) == 9000

Answer: assert Solution().minTime(skill = [1000, 2000, 3000, 4000, 5000], mana = [1000, 2000, 3000, 4000, 5000]) == 95000000

Answer: assert Solution().minTime(skill = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], mana = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 2660

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], mana = [5000, 5000, 5000, 5000, 5000]) == 475000

Answer: assert Solution().minTime(skill = [100, 200, 300, 400, 500, 600], mana = [600, 500, 400, 300, 200, 100]) == 2160000

Answer: assert Solution().minTime(skill = [10, 20, 30, 40, 50], mana = [5, 10, 15, 20, 25, 30]) == 6250

Answer: assert Solution().minTime(skill = [25, 50, 75, 100, 125, 150, 175, 200, 225, 250], mana = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 1787500

Answer: assert Solution().minTime(skill = [100, 200, 300], mana = [50, 25, 75, 100]) == 100000

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5], mana = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 2950

Answer: assert Solution().minTime(skill = [5,3,8,2,4], mana = [15,25,10,40,5]) == 1395

Answer: assert Solution().minTime(skill = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 1771

Answer: assert Solution().minTime(skill = [29, 65, 12, 48, 77], mana = [31, 89, 17, 63, 54, 20, 41, 73]) == 54255

Answer: assert Solution().minTime(skill = [1, 5, 10, 20, 50, 100, 200], mana = [1, 2, 3, 4, 5, 6, 7]) == 5786

Answer: assert Solution().minTime(skill = [1500, 1500, 1500, 1500], mana = [2500, 2500, 2500, 2500, 2500]) == 30000000

Answer: assert Solution().minTime(skill = [4000, 3000, 2000, 1000], mana = [1000, 2000, 3000, 4000, 5000]) == 90000000

Answer: assert Solution().minTime(skill = [100, 200, 300, 400, 500], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 29500

Answer: assert Solution().minTime(skill = [3,6,9,12], mana = [10,20,30,40,50]) == 2100

Answer: assert Solution().minTime(skill = [1, 1, 1, 1, 1], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 95

Answer: assert Solution().minTime(skill = [1000, 2000, 3000], mana = [500, 1000, 1500, 2000, 2500]) == 24500000

Answer: assert Solution().minTime(skill = [100, 150, 200, 250, 300], mana = [50, 100, 150, 200, 250, 300, 350]) == 505000

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], mana = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 7150

Answer: assert Solution().minTime(skill = [7,14,21,28], mana = [2,4,6,8,10,12,14,16]) == 2156

Answer: assert Solution().minTime(skill = [2, 4, 6, 8, 10, 12], mana = [1, 3, 5, 7, 9, 11, 13, 15]) == 908

Answer: assert Solution().minTime(skill = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50], mana = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 17875

Answer: assert Solution().minTime(skill = [3000, 2500, 2000, 1500], mana = [1000, 1200, 1400, 1600, 1800]) == 31800000

Answer: assert Solution().minTime(skill = [500, 1000, 1500, 2000], mana = [200, 400, 600, 800, 1000, 1200]) == 9400000

Answer: assert Solution().minTime(skill = [100, 100, 100, 100, 100], mana = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 140000

Answer: assert Solution().minTime(skill = [2, 4, 6, 8, 10, 12], mana = [12, 10, 8, 6, 4, 2]) == 864

Answer: assert Solution().minTime(skill = [100, 200, 150, 50, 250], mana = [50, 75, 100, 125, 150]) == 172500

Answer: assert Solution().minTime(skill = [2, 4, 6, 8, 10], mana = [1, 3, 5, 7, 9]) == 330

Answer: assert Solution().minTime(skill = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], mana = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 35750

Answer: assert Solution().minTime(skill = [4, 2, 6, 5, 1], mana = [9, 3, 7, 8, 2, 10]) == 465

Answer: assert Solution().minTime(skill = [2,4,6,8,10], mana = [1,1,1,1,1,1,1,1,1,1]) == 120

Answer: assert Solution().minTime(skill = [5000, 5000, 5000, 5000], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 425000

Answer: assert Solution().minTime(skill = [1, 3, 2, 4, 5], mana = [2, 1, 3, 4, 5]) == 115

Answer: assert Solution().minTime(skill = [5, 10, 15, 20, 25], mana = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1500

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 715

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], mana = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 71500

Answer: assert Solution().minTime(skill = [100, 200, 150, 50], mana = [300, 250, 400, 100, 350]) == 440000

Answer: assert Solution().minTime(skill = [50, 40, 30, 20, 10], mana = [25, 20, 15, 10, 5]) == 4750

Answer: assert Solution().minTime(skill = [100, 200, 300, 400], mana = [10, 20, 30, 40, 50, 60]) == 94000

Answer: assert Solution().minTime(skill = [7, 14, 21, 28, 35], mana = [35, 28, 21, 14, 7]) == 6125

Answer: assert Solution().minTime(skill = [42, 15, 88, 34, 99, 56], mana = [72, 33, 19, 55, 48, 62, 28]) == 53845

Answer: assert Solution().minTime(skill = [2500,1000,5000,3000], mana = [5000,2000,1000,3000,4000]) == 115000000

Answer: assert Solution().minTime(skill = [500, 1000, 1500, 2000], mana = [500, 1000, 1500, 2000, 2500]) == 17500000

Answer: assert Solution().minTime(skill = [10, 20, 30, 40, 50], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 2950

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5], mana = [5, 10, 15, 20, 25]) == 475

Answer: assert Solution().minTime(skill = [3, 7, 5, 2, 8], mana = [4, 6, 2, 9, 1]) == 377

Answer: assert Solution().minTime(skill = [5, 3, 8, 6, 2], mana = [7, 1, 4, 2, 9, 5, 3]) == 469

Answer: assert Solution().minTime(skill = [500, 1000, 1500, 2000], mana = [100, 200, 300, 400, 500, 600, 700, 800]) == 7700000

Answer: assert Solution().minTime(skill = [1000,2000,3000,4000,5000], mana = [1,2,3,4,5,6,7,8,9,10]) == 295000

Answer: assert Solution().minTime(skill = [1000, 2000, 3000, 4000, 5000], mana = [1, 10, 100, 1000, 10000]) == 151111000

Answer: assert Solution().minTime(skill = [10, 15, 20, 25, 30], mana = [35, 40, 45, 50, 55, 60, 65, 70]) == 15050

Answer: assert Solution().minTime(skill = [100,200,300,400], mana = [5,10,15,20,25,30]) == 47000

Answer: assert Solution().minTime(skill = [1000, 2000, 3000, 4000, 5000], mana = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 6200000

Answer: assert Solution().minTime(skill = [300, 200, 100], mana = [5, 15, 25, 35, 45, 55]) == 70500

Answer: assert Solution().minTime(skill = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], mana = [19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 3439

Answer: assert Solution().minTime(skill = [2, 5, 7, 8], mana = [1, 3, 6, 9, 12]) == 341

Answer: assert Solution().minTime(skill = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], mana = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 715000

Answer: assert Solution().minTime(skill = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], mana = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1000

Answer: assert Solution().minTime(skill = [100, 200, 300, 400], mana = [50, 60, 70, 80, 90]) == 170000

Answer: assert Solution().minTime(skill = [100, 200, 300, 400, 500], mana = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 147500

Answer: assert Solution().minTime(skill = [300, 200, 100], mana = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 40500

Answer: assert Solution().minTime(skill = [3, 7, 2, 8], mana = [6, 4, 9, 1, 5]) == 356

Answer: assert Solution().minTime(skill = [1, 3, 2, 4], mana = [2, 3, 4, 5]) == 74

Answer: assert Solution().minTime(skill = [1,10,100,1000], mana = [1,10,100,1000,10000]) == 11111111

Answer: assert Solution().minTime(skill = [5, 10, 15, 20, 25, 30], mana = [1, 3, 5, 7, 9]) == 1095

Answer: assert Solution().minTime(skill = [1, 1, 1, 1, 1], mana = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 24

Answer: assert Solution().minTime(skill = [500, 1000, 1500, 2000, 2500], mana = [250, 500, 750, 1000, 1250]) == 11875000

Answer: assert Solution().minTime(skill = [3, 6, 9, 12, 15], mana = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 1770

Answer: assert Solution().minTime(skill = [5000, 4000, 3000, 2000, 1000], mana = [1000, 2000, 3000, 4000, 5000]) == 125000000

Answer: assert Solution().minTime(skill = [1, 10, 100, 1000, 5000], mana = [1, 10, 100, 1000, 5000]) == 31111111

Answer: assert Solution().minTime(skill = [4000, 3000, 2000, 1000, 500], mana = [500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000]) == 142500000

Answer: assert Solution().minTime(skill = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], mana = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 2660

Answer: assert Solution().minTime(skill = [3, 5, 7, 9], mana = [2, 4, 6, 8]) == 238

Answer: assert Solution().minTime(skill = [5000, 1000, 2000, 3000, 4000], mana = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 37500000

Answer: assert Solution().minTime(skill = [1500, 1500, 1500, 1500], mana = [500, 1000, 1500, 2000, 2500, 3000]) == 29250000

Answer: assert Solution().minTime(skill = [2, 3, 5, 7, 11], mana = [13, 17, 19, 23, 29, 31, 37]) == 2080

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 minTime(self, skill: list[int], mana: list[int]) -> int:
    sumSkill = sum(skill)
    prevWizardDone = sumSkill * mana[0]

    for j in range(1, len(mana)):
      prevPotionDone = prevWizardDone
      for i in range(len(skill) - 2, -1, -1):
        # start time for wizard i brewing potion j
        # = max(end time for wizard i brewing potion j - 1,
        #       the earliest start time for wizard i + 1 brewing potion j
        #       (coming from previous iteration)
        #       - time for wizard i brewing potion j)
        prevPotionDone -= skill[i + 1] * mana[j - 1]
        prevWizardDone = max(prevPotionDone,
                             prevWizardDone - skill[i] * mana[j])
      prevWizardDone += sumSkill * mana[j]

    return prevWizardDone