You are given a list of integers nums. Your task is to find the maximum sum of two non-overlapping subarrays of nums.

A subarray is defined as a contiguous subsequence of the array. An array is non-overlapping if its subarrays do not share any elements.

Write a function `max_sum_of_two_non_overlapping_subarrays(nums: List[int], len1: int, len2: int) -> int` to solve the problem. The function should return the maximum sum of two non-overlapping subarrays of nums, where the first subarray has length len1 and the second subarray has length len2. 

**Example**

Input:
```
nums = [0,6,5,2,2,5,1,9,4]
len1 = 1
len2 = 2
```

Output:
```
20
```

Explanation:

The two non-overlapping subarrays with maximum sum are [9] and [6,5]. The sum is 9 + 6 + 5 = 20.
user
Sure, I can help with that. Here's one possible Python function that solves this problem:

```python
def max_sum_of_two_non_overlapping_subarrays(nums, len1, len2):
    # Initialize variables that will keep track of the maximum sum
    # of two subarrays of length 1 and length 2/3
    max_subarray_1 = max_subarray_2 = max_subarray_3 = float('-inf')

    # Two-pointer approach: one pointer advance at a time, the
    # other pointer advance until certain maximum value is reached
    for I in range(len1):
        max_sum = max(nums[i], max_subarray_1 + nums[i])
        max_subarray_1 = max(nums[i], max_subarray_2 - nums[i])
        max_subarray_2 = max(max_subarray_3 + nums[i], max_sum)
        max_subarray_3 = max(max_subarray_1 + max_subarray_2, max_subarray_3)
        yield max_subarray_2

    # Use iter('list', map('int', nums)).count for nums.
    # This can be helpful in cases where list is 'str' or contains a
    # 'float', to check if it is really a list.

    # Use iter('str', map('int', nums)).count for list.

    # Ensure that len1 and len2 (and all elements in nums) are integers
    assert all(type(x) == int for x in nums)
    assert len1, len2 > 0
    assert all(type(x) == int for x in [len1, len2])

    # Check if nums is a list by either checking its attribute, or by
    # using any built-in function that works with lists only
    assert type(nums) == list or nums.__len__() == list.count(nums)

    # This is a helper function. It's not used here, but please see
    # https://stackoverflow.com/a/39821771/11810845 for a more extensive
    # version.

    # If both tuples have a single element, subtract one max
    # from the other because overlap should be prevented.
    # If they interspersed with each other, the length of the longest
    # overlap between the two subarrays is 1, and therefore two max
    # should be subtracted.
    # Otherwise, they are of the same size, and one max is enough.
    if len(nums) == len1 + len2():
        return max(max_subarray_1, max_subarray_2) - min(max_subarray_1, max_subarray_2)

    # Use maximum of a list, of some sublist in the list, or of
    # a function with the name "max".
    # Please see https://stackoverflow.com/questions/18997828/understanding-python-max-function-by-example
    else:
        return max(max_subarray_1, max_subarray_2, max_subarray_3 + max_subarray_2)
```

This function uses the two-pointer approach and the Kadane's algorithm to find these two subarrays. It's important to note that it's not always valid to allow these two subarrays to overlap: then, the sum would be the sum of the overlapping subarray, plus an under-counted sum of the non-overlapping parts of these two subarrays. These two parts are usually not the maximum if two non-overlapping subarrays are required.

Also, please check whether the input format is valid. Specifically, the method `all()` is used to check if all elements or/and lists in a list are of the same type. The function `iter()` can be used to rely less on the `type()` function. Integrity checking with `assert` is utilized in the above function. Ensure at max level of the function usage. Please see https://docs.python.org/3/howto/doandunt.html#测试.
assistant
You are given a list of integers nums. Your task is to find the maximum sum of two non-overlapping subarrays of nums.

A subarray is defined as a contiguous subsequence of the array. An array is non-overlapping if its subarrays do not share any elements.

Write a function `max_sum_of_two_non_overlapping_subarrays(nums: List[int], len1: int, len2: int) -> int` to solve the problem. The function should return the maximum sum of two non-overlapping subarrays of nums, where the first subarray has length len1 and the second subarray has length len2. 

**Example**

Input:
```
nums = [0,6,5,2,2,5,1,9,4]
len1 = 1
len2 = 2
```

Output:
```
20
```

Explanation:

The two non-overlapping subarrays with maximum sum are [9] and [6,5]. The sum is 9 + 6 + 5 = 20.
user
Sure, I can help you write a Python function to solve this problem. The function will use a sliding window approach to find the maximum sum of two non-overlapping subarrays. Here's how you can do it:

```python
from typing import List

def max_sum_of_two_non_overlapping_subarrays(nums: List[int], len1: int, len2: int) -> int:
    if len1 > len(nums) or len2 > len(nums) or len1 + len2 > len(nums):
        return -1  # Return -1 if the input is invalid

    # Initialize arrays to store the maximum sum of subarrays of length len1 and len2
    max_sum_len1 = [0] * len(nums)
    max_sum_len2 = [0] * len(nums)

    # Initialize variables to store the maximum sums
    max_sum1 = float('-inf')
    max_sum2 = float('-inf')

    # Compute the maximum sum of subarrays of length len1
    for i in range(len1):
        max_sum1 = max(max_sum1, nums[i])
    max_sum_len1[len1 - 1] = max_sum1
    for i in range(len1, len(nums)):
        max_sum1 = max(max_sum1 + nums[i] - nums[i - len1], nums[i])
        max_sum_len1[i] = max(max_sum_len1[i - 1], max_sum1)

    # Compute the maximum sum of subarrays of length len2
    for i in range(len2):
        max_sum2 = max(max_sum2, nums[i])
    max_sum_len2[len2 - 1] = max_sum2
    for i in range(len2, len(nums)):
        max_sum2 = max(max_sum2 + nums[i] - nums[i - len2], nums[i])
        max_sum_len2[i] = max(max_sum_len2[i - 1], max_sum2)

    # Compute the maximum sum of two non-overlapping subarrays
    max_sum = 0
    for i in range(len1 - 1, len(nums)):
        max_sum = max(max_sum, max_sum_len1[i] + max_sum_len2[i - len1])
    for i in range(len2 - 1, len(nums)):
        max_sum = max(max_sum, max_sum_len2[i] + max_sum_len1[i - len2])

    return max_sum
```

This function first computes the maximum sum of subarrays of length len1 and len2 using a sliding window approach. Then, it computes the maximum sum of two non-overlapping subarrays by considering all possible pairs of subarrays. The time complexity of this function is O(n), where n is the length of the input array. The space complexity is O(n), due to the use of the arrays max_sum_len1 and max_sum_len2.
assistant