minimum-array-length-after-pair-removals

Minimum Array Length After Pair Removals

Prompt:
"""
You are given a 0-indexed sorted array of integers nums.

You can perform the following operation any number of times:

 * Choose two indices, i and j, where i < j, such that nums[i] < nums[j].
 * Then, remove the elements at indices i and j from nums. The remaining elements retain their original order, and the array is re-indexed.

Return an integer that denotes the minimum length of nums after performing the operation any number of times (including zero).

Note that nums is sorted in non-decreasing order.

Example 1:

Input: nums = [1,3,4,9]
Output: 0
Explanation: Initially, nums = [1, 3, 4, 9].
In the first operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 1 < 3.
Remove indices 0 and 1, and nums becomes [4, 9].
For the next operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 4 < 9.
Remove indices 0 and 1, and nums becomes an empty array [].
Hence, the minimum length achievable is 0.

Example 2:

Input: nums = [2,3,6,9]
Output: 0
Explanation: Initially, nums = [2, 3, 6, 9].
In the first operation, we can choose index 0 and 2 because nums[0] < nums[2] <=> 2 < 6.
Remove indices 0 and 2, and nums becomes [3, 9].
For the next operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 3 < 9.
Remove indices 0 and 1, and nums becomes an empty array [].
Hence, the minimum length achievable is 0.

Example 3:

Input: nums = [1,1,2]
Output: 1
Explanation: Initially, nums = [1, 1, 2].
In an operation, we can choose index 0 and 2 because nums[0] < nums[2] <=> 1 < 2.
Remove indices 0 and 2, and nums becomes [1].
It is no longer possible to perform an operation on the array.
Hence, the minimum achievable length is 1.

Constraints:

 * 1 <= nums.length <= 105
 * 1 <= nums[i] <= 109
 * nums is sorted in non-decreasing order.
"""
class Solution:
    def minLengthAfterRemovals(self, nums: List[int]) -> int:

You are given a 0-indexed sorted array of integers nums.

You can perform the following operation any number of times:

 * Choose two indices, i and j, where i < j, such that nums[i] < nums[j].
 * Then, remove the elements at indices i and j from nums. The remaining elements retain their original order, and the array is re-indexed.

Return an integer that denotes the minimum length of nums after performing the operation any number of times (including zero).

Note that nums is sorted in non-decreasing order.

Example 1:

Input: nums = [1,3,4,9]
Output: 0
Explanation: Initially, nums = [1, 3, 4, 9].
In the first operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 1 < 3.
Remove indices 0 and 1, and nums becomes [4, 9].
For the next operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 4 < 9.
Remove indices 0 and 1, and nums becomes an empty array [].
Hence, the minimum length achievable is 0.

Example 2:

Input: nums = [2,3,6,9]
Output: 0
Explanation: Initially, nums = [2, 3, 6, 9].
In the first operation, we can choose index 0 and 2 because nums[0] < nums[2] <=> 2 < 6.
Remove indices 0 and 2, and nums becomes [3, 9].
For the next operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 3 < 9.
Remove indices 0 and 1, and nums becomes an empty array [].
Hence, the minimum length achievable is 0.

Example 3:

Input: nums = [1,1,2]
Output: 1
Explanation: Initially, nums = [1, 1, 2].
In an operation, we can choose index 0 and 2 because nums[0] < nums[2] <=> 1 < 2.
Remove indices 0 and 2, and nums becomes [1].
It is no longer possible to perform an operation on the array.
Hence, the minimum achievable length is 1.

Constraints:

 * 1 <= nums.length <= 105
 * 1 <= nums[i] <= 109
 * nums is sorted in non-decreasing order.

Please complete the code below to solve above prblem:
```python
class Solution:
    def minLengthAfterRemovals(self, nums: List[int]) -> int:

```

my_solution = Solution()

test_input = { "nums": [1,3,4,9] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [2,3,6,9] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 2

test_input = { "nums": [1,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [2,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 2

test_input = { "nums": [4,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 3

test_input = { "nums": [1,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 3

test_input = { "nums": [2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [2,3,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [3,4,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 4

test_input = { "nums": [1,1,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [2,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 2

test_input = { "nums": [1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 5

test_input = { "nums": [1,1,2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,5,6] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,3,3,3,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [2,3,4,4,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 6

test_input = { "nums": [1,1,2,3,4,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,4,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,2,2,2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,2,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 2

test_input = { "nums": [3,4,7,8,9,9] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 7

test_input = { "nums": [1,1,1,1,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,2,2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,2,3,3,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,3,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,2,3,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 3

test_input = { "nums": [2,2,2,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 8

test_input = { "nums": [1,1,1,1,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,2,2,3,3,4,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,3,4,4,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,2,2,2,4,4,4,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [2,3,3,3,4,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 9

test_input = { "nums": [1,1,1,1,1,1,1,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 5

test_input = { "nums": [1,1,1,1,2,2,2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,2,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 3

test_input = { "nums": [1,1,1,5,5,5,5,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 3

test_input = { "nums": [1,1,2,2,2,2,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,2,2,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,2,4,4,5,5,5,6,6] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 10

test_input = { "nums": [1,1,1,1,1,2,2,2,3,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,2,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 2

test_input = { "nums": [1,1,2,2,2,3,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,2,2,2,3,3,3,3,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,2,2,4,5,6,6,7,7,8] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 11

test_input = { "nums": [1,1,1,1,1,1,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,2,2,2,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 5

test_input = { "nums": [1,1,1,2,2,2,3,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,2,2,3,4,6,6,8,8] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,2,2,2,2,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,2,2,2,3,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,2,2,2,3,3,3,4,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,2,2,2,3,3,4,5,5,6,6] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 12

test_input = { "nums": [1,1,1,1,1,1,1,1,1,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 6

test_input = { "nums": [1,1,1,1,1,2,2,3,3,4,4,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,2,2,2,2,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 6

test_input = { "nums": [1,1,1,2,2,3,3,3,4,5,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,2,4,4,4,4,4,5,6,6] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,2,2,2,2,2,2,2,2,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 4

test_input = { "nums": [1,1,2,2,2,2,2,3,3,3,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,2,2,2,3,3,4,4,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,1,1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 13

test_input = { "nums": [1,1,1,1,1,1,1,2,2,4,4,4,4] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,1,2,3,3,3,3,3,3,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,2,2,2,2,2,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,2,2,3,3,3,3,4,4,4,6,7] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,2,2,2,2,2,2,3,3,4,6,7,7] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,1,1,1,1,1,1,1,1,1,1,1] }
assert my_solution.minLengthAfterRemovals(**test_input) == 14

test_input = { "nums": [1,1,1,1,1,1,2,2,2,2,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,1,2,2,2,2,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 4

test_input = { "nums": [1,1,1,2,2,2,3,3,3,4,4,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,2,2,3,3,3,3,4,4,5,5,6] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,2,2,2,3,3,3,5,6,7,9,9,10] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,3,3,3,3,3,3,3,4,4,4,4,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [2,2,2,2,2,2,2,3,3,3,3,3,3,3] }
assert my_solution.minLengthAfterRemovals(**test_input) == 0

test_input = { "nums": [1,1,1,1,1,1,1,1,1,1,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 5

test_input = { "nums": [1,1,1,1,1,1,1,1,1,2,2,2,2,2,2] }
assert my_solution.minLengthAfterRemovals(**test_input) == 3

test_input = { "nums": [1,1,1,1,1,1,2,2,2,4,4,4,5,5,5] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1

test_input = { "nums": [1,1,1,3,5,6,6,7,7,8,8,8,8,9,9] }
assert my_solution.minLengthAfterRemovals(**test_input) == 1


count-pairs-of-points-with-distance-k

Count Pairs of Points With Distance k

Prompt:
"""
You are given a 2D integer array coordinates and an integer k, where coordinates[i] = [xi, yi] are the coordinates of the ith point in a 2D plane.

We define the distance between two points (x1, y1) and (x2, y2) as (x1 XOR x2) + (y1 XOR y2) where XOR is the bitwise XOR operation.

Return the number of pairs (i, j) such that i < j and the distance between points i and j is equal to k.

Example 1:

Input: coordinates = [[1,2],[4,2],[1,3],[5,2]], k = 5
Output: 2
Explanation: We can choose the following pairs:
- (0,1): Because we have (1 XOR 4) + (2 XOR 2) = 5.
- (2,3): Because we have (1 XOR 5) + (3 XOR 2) = 5.

Example 2:

Input: coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]], k = 0
Output: 10
Explanation: Any two chosen pairs will have a distance of 0. There are 10 ways to choose two pairs.

Constraints:

 * 2 <= coordinates.length <= 50000
 * 0 <= xi, yi <= 106
 * 0 <= k <= 100
"""
class Solution:
    def countPairs(self, coordinates: List[List[int]], k: int) -> int:

You are given a 2D integer array coordinates and an integer k, where coordinates[i] = [xi, yi] are the coordinates of the ith point in a 2D plane.

We define the distance between two points (x1, y1) and (x2, y2) as (x1 XOR x2) + (y1 XOR y2) where XOR is the bitwise XOR operation.

Return the number of pairs (i, j) such that i < j and the distance between points i and j is equal to k.

Example 1:

Input: coordinates = [[1,2],[4,2],[1,3],[5,2]], k = 5
Output: 2
Explanation: We can choose the following pairs:
- (0,1): Because we have (1 XOR 4) + (2 XOR 2) = 5.
- (2,3): Because we have (1 XOR 5) + (3 XOR 2) = 5.

Example 2:

Input: coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]], k = 0
Output: 10
Explanation: Any two chosen pairs will have a distance of 0. There are 10 ways to choose two pairs.

Constraints:

 * 2 <= coordinates.length <= 50000
 * 0 <= xi, yi <= 106
 * 0 <= k <= 100

Please complete the code below to solve above prblem:
```python
class Solution:
    def countPairs(self, coordinates: List[List[int]], k: int) -> int:

```


minimum-edge-reversals-so-every-node-is-reachable

Minimum Edge Reversals So Every Node Is Reachable

Prompt:
"""
There is a simple directed graph with n nodes labeled from 0 to n - 1. The graph would form a tree if its edges were bi-directional.

You are given an integer n and a 2D integer array edges, where edges[i] = [ui, vi] represents a directed edge going from node ui to node vi.

An edge reversal changes the direction of an edge, i.e., a directed edge going from node ui to node vi becomes a directed edge going from node vi to node ui.

For every node i in the range [0, n - 1], your task is to independently calculate the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

Return an integer array answer, where answer[i] is the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

Example 1:

[https://assets.leetcode.com/uploads/2023/08/26/image-20230826221104-3.png]

Input: n = 4, edges = [[2,0],[2,1],[1,3]]
Output: [1,1,0,2]
Explanation: The image above shows the graph formed by the edges.
For node 0: after reversing the edge [2,0], it is possible to reach any other node starting from node 0.
So, answer[0] = 1.
For node 1: after reversing the edge [2,1], it is possible to reach any other node starting from node 1.
So, answer[1] = 1.
For node 2: it is already possible to reach any other node starting from node 2.
So, answer[2] = 0.
For node 3: after reversing the edges [1,3] and [2,1], it is possible to reach any other node starting from node 3.
So, answer[3] = 2.

Example 2:

[https://assets.leetcode.com/uploads/2023/08/26/image-20230826225541-2.png]

Input: n = 3, edges = [[1,2],[2,0]]
Output: [2,0,1]
Explanation: The image above shows the graph formed by the edges.
For node 0: after reversing the edges [2,0] and [1,2], it is possible to reach any other node starting from node 0.
So, answer[0] = 2.
For node 1: it is already possible to reach any other node starting from node 1.
So, answer[1] = 0.
For node 2: after reversing the edge [1, 2], it is possible to reach any other node starting from node 2.
So, answer[2] = 1.

Constraints:

 * 2 <= n <= 105
 * edges.length == n - 1
 * edges[i].length == 2
 * 0 <= ui == edges[i][0] < n
 * 0 <= vi == edges[i][1] < n
 * ui != vi
 * The input is generated such that if the edges were bi-directional, the graph would be a tree.
"""
class Solution:
    def minEdgeReversals(self, n: int, edges: List[List[int]]) -> List[int]:

There is a simple directed graph with n nodes labeled from 0 to n - 1. The graph would form a tree if its edges were bi-directional.

You are given an integer n and a 2D integer array edges, where edges[i] = [ui, vi] represents a directed edge going from node ui to node vi.

An edge reversal changes the direction of an edge, i.e., a directed edge going from node ui to node vi becomes a directed edge going from node vi to node ui.

For every node i in the range [0, n - 1], your task is to independently calculate the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

Return an integer array answer, where answer[i] is the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

Example 1:

[https://assets.leetcode.com/uploads/2023/08/26/image-20230826221104-3.png]

Input: n = 4, edges = [[2,0],[2,1],[1,3]]
Output: [1,1,0,2]
Explanation: The image above shows the graph formed by the edges.
For node 0: after reversing the edge [2,0], it is possible to reach any other node starting from node 0.
So, answer[0] = 1.
For node 1: after reversing the edge [2,1], it is possible to reach any other node starting from node 1.
So, answer[1] = 1.
For node 2: it is already possible to reach any other node starting from node 2.
So, answer[2] = 0.
For node 3: after reversing the edges [1,3] and [2,1], it is possible to reach any other node starting from node 3.
So, answer[3] = 2.

Example 2:

[https://assets.leetcode.com/uploads/2023/08/26/image-20230826225541-2.png]

Input: n = 3, edges = [[1,2],[2,0]]
Output: [2,0,1]
Explanation: The image above shows the graph formed by the edges.
For node 0: after reversing the edges [2,0] and [1,2], it is possible to reach any other node starting from node 0.
So, answer[0] = 2.
For node 1: it is already possible to reach any other node starting from node 1.
So, answer[1] = 0.
For node 2: after reversing the edge [1, 2], it is possible to reach any other node starting from node 2.
So, answer[2] = 1.

Constraints:

 * 2 <= n <= 105
 * edges.length == n - 1
 * edges[i].length == 2
 * 0 <= ui == edges[i][0] < n
 * 0 <= vi == edges[i][1] < n
 * ui != vi
 * The input is generated such that if the edges were bi-directional, the graph would be a tree.

Please complete the code below to solve above prblem:
```python
class Solution:
    def minEdgeReversals(self, n: int, edges: List[List[int]]) -> List[int]:

```

my_solution = Solution()

test_input = { "n": 4, "edges": [[2,0],[2,1],[1,3]] }
assert my_solution.minEdgeReversals(**test_input) == [1,1,0,2]

test_input = { "n": 3, "edges": [[1,2],[2,0]] }
assert my_solution.minEdgeReversals(**test_input) == [2,0,1]

test_input = { "n": 2, "edges": [[0,1]] }
assert my_solution.minEdgeReversals(**test_input) == [0,1]

test_input = { "n": 3, "edges": [[2,0],[2,1]] }
assert my_solution.minEdgeReversals(**test_input) == [1,1,0]

test_input = { "n": 4, "edges": [[0,1],[3,0],[2,3]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,0,1]

test_input = { "n": 4, "edges": [[0,2],[0,3],[3,1]] }
assert my_solution.minEdgeReversals(**test_input) == [0,2,1,1]

test_input = { "n": 4, "edges": [[0,3],[1,2],[2,3]] }
assert my_solution.minEdgeReversals(**test_input) == [2,1,2,3]

test_input = { "n": 4, "edges": [[0,3],[1,2],[3,1]] }
assert my_solution.minEdgeReversals(**test_input) == [0,2,3,1]

test_input = { "n": 4, "edges": [[0,3],[2,1],[3,1]] }
assert my_solution.minEdgeReversals(**test_input) == [1,3,2,2]

test_input = { "n": 4, "edges": [[1,0],[2,0],[3,2]] }
assert my_solution.minEdgeReversals(**test_input) == [3,2,2,1]

test_input = { "n": 5, "edges": [[0,1],[0,4],[2,3],[4,2]] }
assert my_solution.minEdgeReversals(**test_input) == [0,1,2,3,1]

test_input = { "n": 5, "edges": [[0,1],[2,0],[0,4],[3,4]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,1,2,3]

test_input = { "n": 5, "edges": [[0,2],[0,1],[3,1],[4,1]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,3,2,2]

test_input = { "n": 5, "edges": [[0,2],[0,1],[3,1],[4,3]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,3,2,1]

test_input = { "n": 5, "edges": [[0,2],[1,3],[1,4],[2,4]] }
assert my_solution.minEdgeReversals(**test_input) == [1,2,2,3,3]

test_input = { "n": 5, "edges": [[0,2],[1,3],[2,3],[4,2]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,3,4,2]

test_input = { "n": 5, "edges": [[0,2],[2,1],[2,3],[4,3]] }
assert my_solution.minEdgeReversals(**test_input) == [1,3,2,3,2]

test_input = { "n": 5, "edges": [[0,3],[0,4],[1,2],[4,1]] }
assert my_solution.minEdgeReversals(**test_input) == [0,2,3,1,1]

test_input = { "n": 5, "edges": [[1,0],[3,0],[0,4],[2,3]] }
assert my_solution.minEdgeReversals(**test_input) == [3,2,1,2,4]

test_input = { "n": 5, "edges": [[3,0],[0,4],[1,3],[2,3]] }
assert my_solution.minEdgeReversals(**test_input) == [3,1,1,2,4]

test_input = { "n": 6, "edges": [[0,1],[0,5],[1,2],[3,2],[2,4]] }
assert my_solution.minEdgeReversals(**test_input) == [1,2,3,2,4,2]

test_input = { "n": 6, "edges": [[0,1],[2,1],[1,5],[2,3],[4,3]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,2,3,2,4]

test_input = { "n": 6, "edges": [[0,2],[0,3],[0,1],[0,5],[1,4]] }
assert my_solution.minEdgeReversals(**test_input) == [0,1,1,1,2,1]

test_input = { "n": 6, "edges": [[0,2],[1,3],[1,2],[2,4],[2,5]] }
assert my_solution.minEdgeReversals(**test_input) == [1,1,2,2,3,3]

test_input = { "n": 6, "edges": [[0,4],[1,2],[3,1],[5,1],[4,5]] }
assert my_solution.minEdgeReversals(**test_input) == [1,4,5,3,2,3]

test_input = { "n": 6, "edges": [[1,0],[0,4],[2,4],[2,3],[3,5]] }
assert my_solution.minEdgeReversals(**test_input) == [2,1,2,3,3,4]

test_input = { "n": 6, "edges": [[1,0],[3,1],[1,4],[2,5],[4,5]] }
assert my_solution.minEdgeReversals(**test_input) == [3,2,3,1,3,4]

test_input = { "n": 7, "edges": [[0,5],[2,0],[1,3],[6,2],[4,3],[3,5]] }
assert my_solution.minEdgeReversals(**test_input) == [5,4,4,5,4,6,3]

test_input = { "n": 7, "edges": [[0,6],[2,1],[6,1],[2,5],[5,3],[6,4]] }
assert my_solution.minEdgeReversals(**test_input) == [1,3,2,4,3,3,2]

test_input = { "n": 7, "edges": [[5,0],[2,0],[6,1],[2,4],[2,3],[3,6]] }
assert my_solution.minEdgeReversals(**test_input) == [2,4,1,2,2,1,3]

test_input = { "n": 8, "edges": [[0,4],[0,3],[7,0],[1,4],[2,5],[2,3],[6,5]] }
assert my_solution.minEdgeReversals(**test_input) == [4,4,4,5,5,5,4,3]

test_input = { "n": 8, "edges": [[0,5],[1,0],[1,6],[1,2],[2,3],[2,7],[4,7]] }
assert my_solution.minEdgeReversals(**test_input) == [2,1,2,3,2,3,2,3]

test_input = { "n": 8, "edges": [[1,0],[7,1],[2,6],[5,2],[3,6],[5,4],[5,7]] }
assert my_solution.minEdgeReversals(**test_input) == [4,3,2,2,2,1,3,2]

test_input = { "n": 8, "edges": [[2,0],[5,0],[3,1],[1,4],[6,2],[4,5],[7,5]] }
assert my_solution.minEdgeReversals(**test_input) == [7,4,6,3,5,6,5,5]

test_input = { "n": 8, "edges": [[4,0],[0,1],[1,3],[3,2],[6,2],[2,7],[5,7]] }
assert my_solution.minEdgeReversals(**test_input) == [3,4,6,5,2,6,5,7]

test_input = { "n": 8, "edges": [[4,0],[7,1],[2,3],[7,2],[5,3],[4,6],[7,6]] }
assert my_solution.minEdgeReversals(**test_input) == [3,3,3,4,2,3,3,2]

test_input = { "n": 9, "edges": [[0,5],[0,2],[0,7],[0,4],[7,1],[3,2],[6,3],[8,4]] }
assert my_solution.minEdgeReversals(**test_input) == [3,5,4,3,4,4,2,4,3]

test_input = { "n": 9, "edges": [[0,5],[0,6],[0,2],[5,1],[7,2],[4,2],[3,6],[8,4]] }
assert my_solution.minEdgeReversals(**test_input) == [4,6,5,4,4,5,5,4,3]

test_input = { "n": 9, "edges": [[0,5],[7,0],[1,6],[1,3],[2,8],[3,4],[3,7],[7,8]] }
assert my_solution.minEdgeReversals(**test_input) == [4,1,3,2,3,5,2,3,4]

test_input = { "n": 9, "edges": [[2,0],[1,6],[1,5],[2,3],[2,5],[4,5],[5,7],[8,7]] }
assert my_solution.minEdgeReversals(**test_input) == [4,3,3,4,3,4,4,5,4]

test_input = { "n": 9, "edges": [[7,0],[0,6],[1,2],[2,6],[3,6],[4,5],[5,8],[8,6]] }
assert my_solution.minEdgeReversals(**test_input) == [7,6,7,7,5,6,8,6,7]

test_input = { "n": 10, "edges": [[0,1],[0,2],[2,4],[6,2],[3,9],[5,4],[4,8],[5,7],[9,6]] }
assert my_solution.minEdgeReversals(**test_input) == [4,5,5,2,6,5,4,6,7,3]

test_input = { "n": 10, "edges": [[0,3],[0,5],[0,1],[8,1],[6,1],[2,3],[4,6],[9,4],[5,7]] }
assert my_solution.minEdgeReversals(**test_input) == [5,6,5,6,4,6,5,7,5,3]

test_input = { "n": 10, "edges": [[0,5],[1,3],[1,9],[2,7],[4,2],[6,3],[3,4],[5,4],[7,8]] }
assert my_solution.minEdgeReversals(**test_input) == [3,3,6,4,5,4,3,7,8,4]

test_input = { "n": 10, "edges": [[1,0],[0,5],[6,0],[2,3],[4,2],[2,6],[8,2],[2,9],[8,7]] }
assert my_solution.minEdgeReversals(**test_input) == [5,4,3,4,2,6,4,3,2,4]

test_input = { "n": 10, "edges": [[6,0],[7,0],[4,1],[1,9],[2,7],[9,2],[3,7],[5,7],[8,9]] }
assert my_solution.minEdgeReversals(**test_input) == [9,5,7,7,4,7,8,8,5,6]

test_input = { "n": 10, "edges": [[7,0],[1,2],[1,9],[2,3],[2,8],[5,3],[4,6],[6,7],[7,9]] }
assert my_solution.minEdgeReversals(**test_input) == [5,4,5,6,2,5,3,4,6,5]

test_input = { "n": 10, "edges": [[7,0],[1,5],[2,6],[8,2],[7,3],[4,5],[5,6],[9,7],[8,9]] }
assert my_solution.minEdgeReversals(**test_input) == [6,3,4,6,3,4,5,5,3,4]

test_input = { "n": 11, "edges": [[0,1],[1,2],[8,1],[2,4],[3,9],[3,7],[6,4],[5,7],[5,6],[10,8]] }
assert my_solution.minEdgeReversals(**test_input) == [5,6,7,6,8,6,7,7,5,7,4]

test_input = { "n": 11, "edges": [[0,3],[0,2],[1,4],[1,5],[2,9],[3,5],[7,6],[7,9],[7,8],[8,10]] }
assert my_solution.minEdgeReversals(**test_input) == [2,3,3,3,4,4,4,3,4,4,5]

test_input = { "n": 11, "edges": [[0,3],[0,7],[0,9],[0,10],[1,4],[4,2],[2,6],[6,3],[5,6],[7,8]] }
assert my_solution.minEdgeReversals(**test_input) == [5,2,4,6,3,4,5,6,7,6,6]

test_input = { "n": 11, "edges": [[2,0],[0,9],[1,5],[2,8],[3,5],[3,8],[9,4],[9,6],[6,10],[7,10]] }
assert my_solution.minEdgeReversals(**test_input) == [4,3,3,3,6,4,6,6,4,5,7]

test_input = { "n": 11, "edges": [[6,0],[0,1],[1,4],[2,8],[9,3],[4,10],[5,8],[5,6],[6,9],[10,7]] }
assert my_solution.minEdgeReversals(**test_input) == [3,4,1,4,5,1,2,7,2,3,6]

test_input = { "n": 11, "edges": [[7,0],[1,0],[1,6],[5,1],[4,2],[8,2],[9,2],[7,3],[5,9],[10,5]] }
assert my_solution.minEdgeReversals(**test_input) == [6,5,6,6,5,4,6,5,5,5,3]

test_input = { "n": 11, "edges": [[8,0],[6,1],[7,1],[1,10],[3,2],[4,3],[3,8],[5,8],[8,9],[9,10]] }
assert my_solution.minEdgeReversals(**test_input) == [7,7,6,5,4,5,6,6,6,7,8]

test_input = { "n": 11, "edges": [[10,0],[1,2],[1,10],[2,8],[3,9],[3,5],[4,6],[7,4],[4,8],[5,8]] }
assert my_solution.minEdgeReversals(**test_input) == [6,4,5,4,5,5,6,4,6,5,5]

test_input = { "n": 12, "edges": [[0,10],[1,3],[1,10],[2,7],[2,11],[3,4],[5,9],[5,11],[6,9],[9,8],[9,10]] }
assert my_solution.minEdgeReversals(**test_input) == [5,5,4,6,7,4,4,5,6,5,6,5]

test_input = { "n": 12, "edges": [[3,0],[10,0],[6,0],[1,9],[3,2],[4,6],[4,7],[5,11],[11,7],[8,10],[9,11]] }
assert my_solution.minEdgeReversals(**test_input) == [9,5,9,8,7,6,8,8,7,6,8,7]

test_input = { "n": 12, "edges": [[4,0],[11,0],[1,9],[1,3],[6,2],[2,7],[2,3],[3,10],[4,10],[5,6],[10,8]] }
assert my_solution.minEdgeReversals(**test_input) == [7,5,5,6,6,3,4,6,8,6,7,6]

test_input = { "n": 12, "edges": [[10,0],[0,3],[1,6],[1,8],[1,5],[2,3],[2,4],[3,5],[4,7],[4,11],[10,9]] }
assert my_solution.minEdgeReversals(**test_input) == [3,4,3,4,4,5,5,5,5,3,2,5]

test_input = { "n": 13, "edges": [[0,5],[1,10],[2,4],[2,7],[10,2],[3,5],[5,12],[11,6],[6,12],[8,10],[8,11],[10,9]] }
assert my_solution.minEdgeReversals(**test_input) == [5,4,6,5,7,6,6,7,4,6,5,5,7]

test_input = { "n": 13, "edges": [[0,11],[1,4],[1,8],[1,3],[3,2],[10,3],[12,3],[12,5],[6,11],[10,7],[9,10],[11,12]] }
assert my_solution.minEdgeReversals(**test_input) == [4,6,8,7,7,7,4,7,7,5,6,5,6]

test_input = { "n": 13, "edges": [[5,0],[0,2],[0,9],[10,1],[6,1],[7,2],[2,6],[3,7],[8,4],[4,11],[4,12],[9,12]] }
assert my_solution.minEdgeReversals(**test_input) == [6,9,7,5,7,5,8,6,6,7,8,8,8]

test_input = { "n": 13, "edges": [[7,0],[3,1],[2,4],[2,8],[10,2],[3,10],[9,5],[5,7],[6,11],[6,12],[12,7],[10,12]] }
assert my_solution.minEdgeReversals(**test_input) == [7,4,5,3,6,5,4,6,6,4,4,5,5]

test_input = { "n": 14, "edges": [[0,1],[0,7],[2,6],[2,8],[11,3],[4,12],[4,11],[5,10],[7,11],[13,7],[8,10],[10,9],[9,12]] }
assert my_solution.minEdgeReversals(**test_input) == [7,8,5,10,8,6,6,8,6,8,7,9,9,7]

test_input = { "n": 14, "edges": [[0,1],[1,2],[2,8],[9,2],[6,2],[13,2],[3,4],[5,4],[7,5],[6,10],[12,6],[11,7],[11,10]] }
assert my_solution.minEdgeReversals(**test_input) == [6,7,8,9,10,9,7,8,9,7,8,7,6,7]

test_input = { "n": 14, "edges": [[0,2],[0,3],[0,13],[1,3],[2,4],[8,2],[11,3],[12,3],[4,6],[5,7],[7,9],[7,11],[10,12]] }
assert my_solution.minEdgeReversals(**test_input) == [7,7,8,8,9,5,10,6,7,7,6,7,7,8]

test_input = { "n": 14, "edges": [[0,4],[0,8],[1,3],[1,13],[2,9],[4,11],[4,12],[5,11],[8,6],[13,6],[7,9],[7,8],[10,8]] }
assert my_solution.minEdgeReversals(**test_input) == [6,6,6,7,7,7,8,6,7,7,6,8,8,7]

test_input = { "n": 14, "edges": [[0,6],[5,0],[2,0],[12,1],[13,2],[12,3],[4,7],[5,7],[7,12],[8,13],[9,11],[9,10],[10,13]] }
assert my_solution.minEdgeReversals(**test_input) == [7,9,6,9,6,6,8,7,4,3,4,4,8,5]

test_input = { "n": 14, "edges": [[0,9],[0,11],[0,5],[1,6],[1,11],[7,2],[3,5],[3,12],[3,13],[11,4],[6,10],[9,7],[11,8]] }
assert my_solution.minEdgeReversals(**test_input) == [2,2,5,2,4,3,3,4,4,3,4,3,3,3]

test_input = { "n": 14, "edges": [[0,11],[1,2],[1,10],[1,6],[3,6],[4,11],[10,4],[5,12],[13,6],[8,7],[8,9],[8,12],[8,13]] }
assert my_solution.minEdgeReversals(**test_input) == [7,5,6,5,7,4,6,5,4,5,6,8,5,5]

test_input = { "n": 14, "edges": [[1,0],[1,8],[7,2],[2,11],[2,13],[3,9],[8,3],[3,11],[4,12],[4,8],[5,11],[6,10],[10,12]] }
assert my_solution.minEdgeReversals(**test_input) == [7,6,8,8,6,8,5,7,7,9,6,9,7,9]

test_input = { "n": 14, "edges": [[1,0],[11,0],[6,0],[7,2],[2,8],[10,3],[4,10],[5,12],[12,6],[13,6],[7,10],[9,8],[8,12]] }
assert my_solution.minEdgeReversals(**test_input) == [11,10,7,8,6,8,10,6,8,7,7,10,9,9]

test_input = { "n": 14, "edges": [[3,0],[5,0],[0,7],[1,8],[1,4],[12,2],[4,3],[10,3],[12,5],[13,6],[7,13],[9,10],[10,11]] }
assert my_solution.minEdgeReversals(**test_input) == [7,4,6,6,5,6,10,8,5,4,5,6,5,9]

test_input = { "n": 15, "edges": [[0,5],[1,9],[4,1],[1,5],[14,1],[2,5],[4,3],[4,6],[5,11],[5,7],[10,6],[7,8],[13,7],[14,12]] }
assert my_solution.minEdgeReversals(**test_input) == [6,6,6,6,5,7,6,8,9,7,5,8,6,7,5]

test_input = { "n": 15, "edges": [[0,6],[13,0],[1,2],[10,1],[3,12],[4,11],[5,12],[10,7],[9,7],[7,13],[11,8],[8,9],[12,11],[13,14]] }
assert my_solution.minEdgeReversals(**test_input) == [10,8,9,3,4,3,11,8,6,7,7,5,4,9,10]

test_input = { "n": 15, "edges": [[0,7],[12,1],[5,2],[4,2],[3,8],[3,14],[12,4],[4,7],[5,6],[10,5],[11,5],[6,9],[7,14],[13,12]] }
assert my_solution.minEdgeReversals(**test_input) == [7,7,8,8,7,7,8,8,9,9,6,6,6,5,9]

test_input = { "n": 15, "edges": [[1,0],[10,1],[2,8],[2,3],[5,3],[4,8],[9,5],[6,12],[7,12],[8,7],[9,11],[11,10],[10,13],[10,14]] }
assert my_solution.minEdgeReversals(**test_input) == [7,6,4,5,4,4,6,6,5,3,5,4,7,6,6]

test_input = { "n": 15, "edges": [[2,0],[0,7],[0,5],[1,6],[1,7],[3,4],[8,4],[10,4],[5,12],[5,10],[11,7],[9,13],[10,14],[13,14]] }
assert my_solution.minEdgeReversals(**test_input) == [7,7,6,9,10,8,8,8,9,8,9,7,9,9,10]

test_input = { "n": 15, "edges": [[8,0],[1,0],[1,13],[1,14],[9,2],[3,13],[4,11],[4,14],[5,8],[12,6],[9,6],[7,8],[14,9],[10,13]] }
assert my_solution.minEdgeReversals(**test_input) == [8,7,10,7,7,6,10,6,7,9,7,8,9,8,8]

test_input = { "n": 15, "edges": [[12,0],[0,8],[1,3],[2,1],[2,7],[12,2],[9,3],[4,11],[11,5],[5,7],[6,13],[6,9],[8,14],[10,12]] }
assert my_solution.minEdgeReversals(**test_input) == [7,8,7,9,5,7,7,8,8,8,5,6,6,8,9]

test_input = { "n": 15, "edges": [[12,0],[1,12],[1,7],[2,12],[3,7],[3,14],[4,6],[5,6],[5,7],[6,8],[6,10],[11,6],[7,13],[9,14]] }
assert my_solution.minEdgeReversals(**test_input) == [8,6,6,6,6,6,7,7,8,6,8,6,7,8,7]

test_input = { "n": 16, "edges": [[0,1],[5,0],[0,2],[0,4],[2,12],[10,3],[3,15],[4,7],[8,6],[6,9],[7,14],[7,13],[11,9],[13,9],[10,13]] }
assert my_solution.minEdgeReversals(**test_input) == [5,6,6,8,6,4,8,7,7,9,7,8,7,8,8,9]

test_input = { "n": 16, "edges": [[2,0],[0,4],[4,1],[1,11],[5,2],[8,3],[4,3],[4,13],[14,4],[7,5],[5,12],[6,9],[12,9],[10,14],[11,15]] }
assert my_solution.minEdgeReversals(**test_input) == [7,9,6,9,8,5,6,4,8,7,6,10,6,9,7,11]

test_input = { "n": 16, "edges": [[8,0],[1,6],[10,1],[8,2],[3,15],[14,4],[12,5],[13,5],[8,6],[6,9],[6,13],[11,7],[7,13],[15,10],[11,14]] }
assert my_solution.minEdgeReversals(**test_input) == [8,7,8,4,9,10,8,8,7,9,6,7,9,9,8,5]

test_input = { "n": 17, "edges": [[0,4],[0,9],[13,1],[5,1],[6,2],[13,2],[3,8],[3,15],[3,9],[4,5],[5,10],[11,6],[7,16],[12,9],[16,9],[12,14]] }
assert my_solution.minEdgeReversals(**test_input) == [7,10,10,7,8,9,9,6,8,8,10,8,7,9,8,8,7]

test_input = { "n": 17, "edges": [[0,7],[15,1],[2,3],[2,7],[3,8],[15,3],[5,4],[4,16],[6,14],[16,7],[16,9],[10,14],[10,16],[16,11],[12,14],[15,13]] }
assert my_solution.minEdgeReversals(**test_input) == [8,9,8,9,7,6,7,9,10,9,7,9,7,9,8,8,8]

test_input = { "n": 17, "edges": [[0,10],[12,0],[0,14],[0,7],[0,16],[1,8],[1,7],[2,8],[3,5],[4,15],[5,9],[11,5],[14,6],[11,7],[15,8],[13,16]] }
assert my_solution.minEdgeReversals(**test_input) == [8,8,8,8,7,9,10,9,9,10,9,8,7,8,9,8,9]

test_input = { "n": 17, "edges": [[0,12],[1,2],[1,13],[1,14],[4,3],[3,15],[5,4],[10,6],[14,6],[6,15],[7,11],[8,11],[13,9],[10,11],[15,12],[16,15]] }
assert my_solution.minEdgeReversals(**test_input) == [11,8,9,10,9,8,10,9,9,10,9,10,12,9,9,11,10]

test_input = { "n": 17, "edges": [[0,13],[15,0],[1,5],[1,6],[11,1],[1,13],[8,2],[3,16],[4,16],[7,14],[11,8],[9,10],[9,16],[14,12],[14,15],[15,16]] }
assert my_solution.minEdgeReversals(**test_input) == [8,8,9,7,7,9,9,5,8,7,8,7,7,9,6,7,8]

test_input = { "n": 17, "edges": [[8,0],[0,10],[6,1],[1,15],[15,2],[3,2],[12,3],[9,4],[5,7],[13,7],[9,10],[10,11],[10,14],[13,12],[16,12],[14,15]] }
assert my_solution.minEdgeReversals(**test_input) == [9,11,13,12,10,10,10,11,8,9,10,11,11,10,11,12,10]

test_input = { "n": 17, "edges": [[10,0],[0,5],[1,8],[1,16],[7,2],[2,8],[3,5],[8,3],[4,11],[13,4],[16,6],[16,9],[14,12],[14,13],[14,15],[15,16]] }
assert my_solution.minEdgeReversals(**test_input) == [8,6,6,8,7,9,8,5,7,8,7,8,6,6,5,6,7]

test_input = { "n": 18, "edges": [[0,3],[16,1],[1,10],[2,13],[2,8],[14,3],[4,12],[5,10],[13,6],[7,11],[10,7],[9,7],[14,8],[9,8],[9,17],[12,14],[13,15]] }
assert my_solution.minEdgeReversals(**test_input) == [9,8,9,10,7,8,11,10,10,9,9,11,8,10,9,11,7,10]

test_input = { "n": 18, "edges": [[0,10],[0,17],[1,3],[1,2],[2,9],[2,17],[16,3],[4,7],[4,13],[4,6],[5,12],[5,17],[6,17],[8,15],[11,8],[16,11],[13,14]] }
assert my_solution.minEdgeReversals(**test_input) == [6,5,6,6,5,6,6,6,7,7,7,6,7,6,7,8,5,7]

test_input = { "n": 18, "edges": [[11,0],[5,1],[1,10],[1,3],[1,17],[14,2],[2,13],[3,13],[4,7],[4,12],[4,17],[6,17],[7,8],[15,9],[16,11],[11,14],[14,15]] }
assert my_solution.minEdgeReversals(**test_input) == [7,7,8,8,7,6,7,8,9,9,8,6,8,9,7,8,5,8]

test_input = { "n": 19, "edges": [[0,3],[0,5],[4,0],[12,1],[1,5],[2,17],[2,4],[3,13],[4,8],[5,7],[18,6],[18,8],[14,9],[9,15],[16,9],[10,12],[11,17],[12,16]] }
assert my_solution.minEdgeReversals(**test_input) == [8,8,6,9,7,9,8,10,8,9,6,6,7,10,8,10,8,7,7]

test_input = { "n": 19, "edges": [[0,5],[0,9],[14,1],[2,11],[3,12],[3,8],[10,3],[4,13],[4,12],[6,17],[10,7],[7,14],[8,11],[16,8],[9,14],[9,17],[15,17],[15,18]] }
assert my_solution.minEdgeReversals(**test_input) == [7,10,9,8,8,8,8,8,9,8,7,10,9,9,9,8,8,9,9]

test_input = { "n": 19, "edges": [[0,12],[13,1],[12,1],[14,2],[2,11],[3,9],[11,3],[15,4],[4,11],[5,12],[17,6],[8,7],[8,10],[16,8],[9,12],[11,18],[16,18],[17,18]] }
assert my_solution.minEdgeReversals(**test_input) == [11,13,8,10,8,11,10,11,10,11,11,9,12,12,7,7,9,9,10]

test_input = { "n": 19, "edges": [[0,18],[8,1],[5,1],[9,2],[6,2],[3,11],[17,3],[4,12],[4,6],[18,4],[14,5],[5,16],[6,7],[16,7],[17,7],[15,8],[10,14],[14,13]] }
assert my_solution.minEdgeReversals(**test_input) == [8,11,12,12,10,10,11,12,10,11,8,13,11,10,9,9,11,11,9]

test_input = { "n": 19, "edges": [[1,0],[0,13],[15,0],[1,9],[5,2],[2,13],[3,12],[3,16],[4,12],[5,7],[8,6],[12,8],[16,10],[13,10],[17,11],[13,11],[14,13],[15,18]] }
assert my_solution.minEdgeReversals(**test_input) == [9,8,9,9,9,8,12,9,11,9,11,11,10,10,9,8,10,10,9]


points-that-intersect-with-cars

Points That Intersect With Cars

Prompt:
"""
You are given a 0-indexed 2D integer array nums representing the coordinates of the cars parking on a number line. For any index i, nums[i] = [starti, endi] where starti is the starting point of the ith car and endi is the ending point of the ith car.

Return the number of integer points on the line that are covered with any part of a car.

Example 1:

Input: nums = [[3,6],[1,5],[4,7]]
Output: 7
Explanation: All the points from 1 to 7 intersect at least one car, therefore the answer would be 7.

Example 2:

Input: nums = [[1,3],[5,8]]
Output: 7
Explanation: Points intersecting at least one car are 1, 2, 3, 5, 6, 7, 8. There are a total of 7 points, therefore the answer would be 7.

Constraints:

 * 1 <= nums.length <= 100
 * nums[i].length == 2
 * 1 <= starti <= endi <= 100
"""
class Solution:
    def numberOfPoints(self, nums: List[List[int]]) -> int:

You are given a 0-indexed 2D integer array nums representing the coordinates of the cars parking on a number line. For any index i, nums[i] = [starti, endi] where starti is the starting point of the ith car and endi is the ending point of the ith car.

Return the number of integer points on the line that are covered with any part of a car.

Example 1:

Input: nums = [[3,6],[1,5],[4,7]]
Output: 7
Explanation: All the points from 1 to 7 intersect at least one car, therefore the answer would be 7.

Example 2:

Input: nums = [[1,3],[5,8]]
Output: 7
Explanation: Points intersecting at least one car are 1, 2, 3, 5, 6, 7, 8. There are a total of 7 points, therefore the answer would be 7.

Constraints:

 * 1 <= nums.length <= 100
 * nums[i].length == 2
 * 1 <= starti <= endi <= 100

Please complete the code below to solve above prblem:
```python
class Solution:
    def numberOfPoints(self, nums: List[List[int]]) -> int:

```


determine-if-a-cell-is-reachable-at-a-given-time

Determine if a Cell Is Reachable at a Given Time

Prompt:
"""
You are given four integers sx, sy, fx, fy, and a non-negative integer t.

In an infinite 2D grid, you start at the cell (sx, sy). Each second, you must move to any of its adjacent cells.

Return true if you can reach cell (fx, fy) after exactly t seconds, or false otherwise.

A cell's adjacent cells are the 8 cells around it that share at least one corner with it. You can visit the same cell several times.

Example 1:

[https://assets.leetcode.com/uploads/2023/08/05/example2.svg]

Input: sx = 2, sy = 4, fx = 7, fy = 7, t = 6
Output: true
Explanation: Starting at cell (2, 4), we can reach cell (7, 7) in exactly 6 seconds by going through the cells depicted in the picture above.

Example 2:

[https://assets.leetcode.com/uploads/2023/08/05/example1.svg]

Input: sx = 3, sy = 1, fx = 7, fy = 3, t = 3
Output: false
Explanation: Starting at cell (3, 1), it takes at least 4 seconds to reach cell (7, 3) by going through the cells depicted in the picture above. Hence, we cannot reach cell (7, 3) at the third second.

Constraints:

 * 1 <= sx, sy, fx, fy <= 109
 * 0 <= t <= 109
"""
class Solution:
    def isReachableAtTime(self, sx: int, sy: int, fx: int, fy: int, t: int) -> bool:

You are given four integers sx, sy, fx, fy, and a non-negative integer t.

In an infinite 2D grid, you start at the cell (sx, sy). Each second, you must move to any of its adjacent cells.

Return true if you can reach cell (fx, fy) after exactly t seconds, or false otherwise.

A cell's adjacent cells are the 8 cells around it that share at least one corner with it. You can visit the same cell several times.

Example 1:

[https://assets.leetcode.com/uploads/2023/08/05/example2.svg]

Input: sx = 2, sy = 4, fx = 7, fy = 7, t = 6
Output: true
Explanation: Starting at cell (2, 4), we can reach cell (7, 7) in exactly 6 seconds by going through the cells depicted in the picture above.

Example 2:

[https://assets.leetcode.com/uploads/2023/08/05/example1.svg]

Input: sx = 3, sy = 1, fx = 7, fy = 3, t = 3
Output: false
Explanation: Starting at cell (3, 1), it takes at least 4 seconds to reach cell (7, 3) by going through the cells depicted in the picture above. Hence, we cannot reach cell (7, 3) at the third second.

Constraints:

 * 1 <= sx, sy, fx, fy <= 109
 * 0 <= t <= 109

Please complete the code below to solve above prblem:
```python
class Solution:
    def isReachableAtTime(self, sx: int, sy: int, fx: int, fy: int, t: int) -> bool:

```

my_solution = Solution()

test_input = { "sx": 3, "sy": 1, "fx": 7, "fy": 3, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 2, "sy": 4, "fx": 7, "fy": 7, "t": 6 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 1, "fy": 2, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 2, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 3, "fy": 4, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 3, "fy": 5, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 1, "fy": 1, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 1, "fy": 3, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 4, "fy": 1, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 4, "fy": 2, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 1, "fy": 4, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 1, "fy": 5, "t": 8 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 2, "fy": 1, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 4, "fy": 3, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 2, "fy": 2, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 4, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 5, "fy": 1, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 2, "fy": 3, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 5, "fy": 2, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 1, "fx": 2, "fy": 5, "t": 6 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 3, "fy": 1, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 3, "fy": 2, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 3, "fy": 3, "t": 9 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 4, "fy": 5, "t": 9 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 5, "fy": 3, "t": 9 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 5, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 1, "fy": 1, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 1, "fx": 5, "fy": 5, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 1, "fy": 2, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 1, "fy": 3, "t": 6 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 1, "fy": 4, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 2, "fy": 5, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 3, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 1, "fy": 5, "t": 5 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 3, "fy": 5, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 4, "fy": 1, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 2, "fy": 1, "t": 10 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 2, "fy": 2, "t": 9 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 2, "fy": 3, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 4, "fy": 2, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 2, "fy": 4, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 4, "fy": 3, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 4, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 3, "fy": 1, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 3, "fy": 2, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 4, "fy": 5, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 3, "fy": 3, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 5, "fy": 1, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 5, "fy": 3, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 2, "fx": 5, "fy": 2, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 5, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 1, "fy": 1, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 1, "fy": 2, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 2, "fx": 5, "fy": 5, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 2, "fy": 1, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 2, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 1, "fy": 3, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 1, "fy": 4, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 1, "fy": 5, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 2, "fy": 2, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 2, "fy": 3, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 3, "fy": 1, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 2, "fy": 5, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 4, "fy": 1, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 3, "fy": 2, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 3, "fy": 3, "t": 8 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 4, "fy": 5, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 5, "fy": 1, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 5, "fy": 2, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 5, "fy": 3, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 5, "fy": 4, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 5, "fy": 5, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 3, "fy": 4, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 3, "fy": 5, "t": 2 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 1, "fy": 2, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 3, "fx": 4, "fy": 2, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 4, "fy": 3, "t": 10 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 3, "fx": 4, "fy": 4, "t": 10 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 1, "fy": 1, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 1, "fy": 3, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 1, "fy": 4, "t": 6 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 2, "fy": 2, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 1, "fy": 5, "t": 6 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 2, "fy": 4, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 2, "fy": 1, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 3, "fy": 3, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 2, "fy": 3, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 2, "fy": 5, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 3, "fy": 1, "t": 4 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 3, "fy": 2, "t": 5 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 4, "fy": 1, "t": 7 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 3, "fy": 4, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 4, "fy": 4, "t": 10 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 4, "fy": 5, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == True

test_input = { "sx": 1, "sy": 4, "fx": 3, "fy": 5, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 4, "fy": 2, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 4, "fy": 3, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 5, "fy": 2, "t": 1 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 5, "fy": 4, "t": 3 }
assert my_solution.isReachableAtTime(**test_input) == False

test_input = { "sx": 1, "sy": 4, "fx": 5, "fy": 5, "t": 0 }
assert my_solution.isReachableAtTime(**test_input) == False


minimum-moves-to-spread-stones-over-grid

Minimum Moves to Spread Stones Over Grid

Prompt:
"""
You are given a 0-indexed 2D integer matrix grid of size 3 * 3, representing the number of stones in each cell. The grid contains exactly 9 stones, and there can be multiple stones in a single cell.

In one move, you can move a single stone from its current cell to any other cell if the two cells share a side.

Return the minimum number of moves required to place one stone in each cell.

Example 1:

[https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg]

Input: grid = [[1,1,0],[1,1,1],[1,2,1]]
Output: 3
Explanation: One possible sequence of moves to place one stone in each cell is:
1- Move one stone from cell (2,1) to cell (2,2).
2- Move one stone from cell (2,2) to cell (1,2).
3- Move one stone from cell (1,2) to cell (0,2).
In total, it takes 3 moves to place one stone in each cell of the grid.
It can be shown that 3 is the minimum number of moves required to place one stone in each cell.

Example 2:

[https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg]

Input: grid = [[1,3,0],[1,0,0],[1,0,3]]
Output: 4
Explanation: One possible sequence of moves to place one stone in each cell is:
1- Move one stone from cell (0,1) to cell (0,2).
2- Move one stone from cell (0,1) to cell (1,1).
3- Move one stone from cell (2,2) to cell (1,2).
4- Move one stone from cell (2,2) to cell (2,1).
In total, it takes 4 moves to place one stone in each cell of the grid.
It can be shown that 4 is the minimum number of moves required to place one stone in each cell.

Constraints:

 * grid.length == grid[i].length == 3
 * 0 <= grid[i][j] <= 9
 * Sum of grid is equal to 9.
"""
class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:

You are given a 0-indexed 2D integer matrix grid of size 3 * 3, representing the number of stones in each cell. The grid contains exactly 9 stones, and there can be multiple stones in a single cell.

In one move, you can move a single stone from its current cell to any other cell if the two cells share a side.

Return the minimum number of moves required to place one stone in each cell.

Example 1:

[https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg]

Input: grid = [[1,1,0],[1,1,1],[1,2,1]]
Output: 3
Explanation: One possible sequence of moves to place one stone in each cell is:
1- Move one stone from cell (2,1) to cell (2,2).
2- Move one stone from cell (2,2) to cell (1,2).
3- Move one stone from cell (1,2) to cell (0,2).
In total, it takes 3 moves to place one stone in each cell of the grid.
It can be shown that 3 is the minimum number of moves required to place one stone in each cell.

Example 2:

[https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg]

Input: grid = [[1,3,0],[1,0,0],[1,0,3]]
Output: 4
Explanation: One possible sequence of moves to place one stone in each cell is:
1- Move one stone from cell (0,1) to cell (0,2).
2- Move one stone from cell (0,1) to cell (1,1).
3- Move one stone from cell (2,2) to cell (1,2).
4- Move one stone from cell (2,2) to cell (2,1).
In total, it takes 4 moves to place one stone in each cell of the grid.
It can be shown that 4 is the minimum number of moves required to place one stone in each cell.

Constraints:

 * grid.length == grid[i].length == 3
 * 0 <= grid[i][j] <= 9
 * Sum of grid is equal to 9.

Please complete the code below to solve above prblem:
```python
class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:

```

my_solution = Solution()

test_input = { "grid": [[1,1,0],[1,1,1],[1,2,1]] }
assert my_solution.minimumMoves(**test_input) == 3

test_input = { "grid": [[1,3,0],[1,0,0],[1,0,3]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[1,2,2],[1,1,0],[0,1,1]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[1,3,3],[1,0,0],[0,1,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[3,2,0],[0,1,0],[0,3,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[1,0,4],[2,0,0],[2,0,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,1,3],[3,1,0],[0,1,0]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[3,0,0],[0,2,1],[1,0,2]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[1,0,0],[4,1,1],[0,2,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,2,3],[2,0,1],[0,1,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[4,0,0],[0,0,2],[3,0,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[3,0,0],[4,1,0],[1,0,0]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[0,2,1],[1,2,0],[3,0,0]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[1,3,0],[0,0,1],[2,1,1]] }
assert my_solution.minimumMoves(**test_input) == 3

test_input = { "grid": [[3,0,0],[1,0,1],[0,2,2]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[4,2,2],[0,1,0],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[3,2,1],[1,1,0],[1,0,0]] }
assert my_solution.minimumMoves(**test_input) == 9

test_input = { "grid": [[0,3,0],[2,0,0],[1,3,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,0,0],[3,0,0],[4,2,0]] }
assert my_solution.minimumMoves(**test_input) == 13

test_input = { "grid": [[1,1,2],[0,0,0],[0,4,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[4,0,0],[0,0,0],[1,2,2]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[1,3,1],[0,0,0],[1,2,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[3,1,0],[1,2,2],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[2,3,2],[0,1,0],[0,0,1]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,1,4],[0,3,0],[0,1,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,1,0],[1,4,0],[0,3,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,0,1],[0,0,3],[2,2,1]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[1,0,1],[1,2,0],[1,0,3]] }
assert my_solution.minimumMoves(**test_input) == 3

test_input = { "grid": [[0,0,0],[4,1,2],[1,1,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[2,2,1],[0,2,1],[0,1,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[1,0,0],[0,2,0],[4,2,0]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[2,0,1],[4,0,0],[0,2,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,0,3],[0,2,0],[1,3,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[2,0,1],[1,0,0],[4,0,1]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,1,0],[1,0,3],[0,3,1]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,3,1],[0,0,0],[3,1,1]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[3,0,1],[0,3,1],[0,0,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[0,4,0],[1,0,0],[0,2,2]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[4,2,0],[0,0,0],[1,1,1]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,2,0],[2,1,2],[0,2,0]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[0,1,0],[2,1,1],[4,0,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,4,1],[1,0,1],[0,0,2]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[1,0,0],[0,0,0],[1,3,4]] }
assert my_solution.minimumMoves(**test_input) == 9

test_input = { "grid": [[0,7,1],[0,1,0],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 13

test_input = { "grid": [[0,1,1],[0,2,1],[2,0,2]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[0,2,0],[3,0,0],[3,1,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,0,0],[2,0,2],[0,2,3]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,3,4],[0,1,0],[1,0,0]] }
assert my_solution.minimumMoves(**test_input) == 9

test_input = { "grid": [[1,0,0],[0,0,1],[7,0,0]] }
assert my_solution.minimumMoves(**test_input) == 13

test_input = { "grid": [[0,0,2],[2,0,0],[1,4,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[2,0,1],[1,3,0],[0,2,0]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[1,0,2],[2,3,0],[1,0,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[1,1,2],[0,0,0],[3,1,1]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[0,2,0],[0,1,0],[0,0,6]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[1,1,1],[3,0,0],[2,1,0]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[2,0,0],[2,0,1],[3,1,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[1,1,0],[0,2,2],[0,3,0]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[1,0,3],[1,1,0],[1,0,2]] }
assert my_solution.minimumMoves(**test_input) == 3

test_input = { "grid": [[1,3,0],[2,0,0],[3,0,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[1,0,1],[0,0,1],[0,1,5]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[2,0,0],[0,2,1],[1,1,2]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[1,2,3],[1,0,1],[0,0,1]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,2,3],[1,0,0],[0,1,2]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[4,1,0],[0,1,1],[2,0,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[2,0,1],[1,0,1],[1,2,1]] }
assert my_solution.minimumMoves(**test_input) == 2

test_input = { "grid": [[3,0,3],[0,0,0],[1,1,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[0,0,0],[3,4,2],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[2,1,2],[0,0,1],[3,0,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[1,0,0],[0,3,3],[0,0,2]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,2,0],[1,0,1],[1,3,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[0,1,0],[2,0,4],[1,0,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[1,0,3],[0,0,2],[0,1,2]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[2,1,1],[0,0,0],[0,1,4]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[2,0,1],[0,2,0],[1,3,0]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[2,0,2],[0,0,2],[0,0,3]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,2,2],[2,0,1],[1,1,0]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[0,0,1],[2,3,2],[1,0,0]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[1,1,0],[3,0,4],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[1,0,0],[0,0,0],[5,1,2]] }
assert my_solution.minimumMoves(**test_input) == 11

test_input = { "grid": [[1,0,0],[3,5,0],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 9

test_input = { "grid": [[3,1,1],[1,1,0],[2,0,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,1,3],[0,0,1],[1,2,1]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,0,0],[1,2,0],[3,0,3]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,0,0],[1,2,2],[2,0,2]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[4,0,0],[2,3,0],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[1,1,0],[1,0,1],[4,1,0]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,0,1],[0,1,2],[1,0,4]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[0,1,3],[2,0,0],[0,3,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,0,0],[5,0,1],[1,1,1]] }
assert my_solution.minimumMoves(**test_input) == 7

test_input = { "grid": [[0,1,1],[0,0,3],[2,1,1]] }
assert my_solution.minimumMoves(**test_input) == 5

test_input = { "grid": [[2,0,1],[0,0,1],[2,2,1]] }
assert my_solution.minimumMoves(**test_input) == 3

test_input = { "grid": [[3,0,2],[2,1,0],[0,0,1]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,0,2],[0,0,2],[4,0,1]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[3,0,0],[0,2,0],[0,0,4]] }
assert my_solution.minimumMoves(**test_input) == 8

test_input = { "grid": [[0,1,3],[1,0,0],[0,4,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[2,1,2],[0,2,1],[1,0,0]] }
assert my_solution.minimumMoves(**test_input) == 4

test_input = { "grid": [[0,0,2],[1,0,3],[1,0,2]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[0,2,2],[0,1,4],[0,0,0]] }
assert my_solution.minimumMoves(**test_input) == 10

test_input = { "grid": [[1,0,1],[0,0,5],[1,1,0]] }
assert my_solution.minimumMoves(**test_input) == 6

test_input = { "grid": [[3,1,0],[0,0,0],[0,1,4]] }
assert my_solution.minimumMoves(**test_input) == 8


string-transformation

String Transformation

Prompt:
"""
You are given two strings s and t of equal length n. You can perform the following operation on the string s:

 * Remove a suffix of s of length l where 0 < l < n and append it at the start of s.
   For example, let s = 'abcd' then in one operation you can remove the suffix 'cd' and append it in front of s making s = 'cdab'.

You are also given an integer k. Return the number of ways in which s can be transformed into t in exactly k operations.

Since the answer can be large, return it modulo 109 + 7.

Example 1:

Input: s = "abcd", t = "cdab", k = 2
Output: 2
Explanation:
First way:
In first operation, choose suffix from index = 3, so resulting s = "dabc".
In second operation, choose suffix from index = 3, so resulting s = "cdab".

Second way:
In first operation, choose suffix from index = 1, so resulting s = "bcda".
In second operation, choose suffix from index = 1, so resulting s = "cdab".

Example 2:

Input: s = "ababab", t = "ababab", k = 1
Output: 2
Explanation:
First way:
Choose suffix from index = 2, so resulting s = "ababab".

Second way:
Choose suffix from index = 4, so resulting s = "ababab".

Constraints:

 * 2 <= s.length <= 5 * 105
 * 1 <= k <= 1015
 * s.length == t.length
 * s and t consist of only lowercase English alphabets.
"""
class Solution:
    def numberOfWays(self, s: str, t: str, k: int) -> int:

You are given two strings s and t of equal length n. You can perform the following operation on the string s:

 * Remove a suffix of s of length l where 0 < l < n and append it at the start of s.
   For example, let s = 'abcd' then in one operation you can remove the suffix 'cd' and append it in front of s making s = 'cdab'.

You are also given an integer k. Return the number of ways in which s can be transformed into t in exactly k operations.

Since the answer can be large, return it modulo 109 + 7.

Example 1:

Input: s = "abcd", t = "cdab", k = 2
Output: 2
Explanation:
First way:
In first operation, choose suffix from index = 3, so resulting s = "dabc".
In second operation, choose suffix from index = 3, so resulting s = "cdab".

Second way:
In first operation, choose suffix from index = 1, so resulting s = "bcda".
In second operation, choose suffix from index = 1, so resulting s = "cdab".

Example 2:

Input: s = "ababab", t = "ababab", k = 1
Output: 2
Explanation:
First way:
Choose suffix from index = 2, so resulting s = "ababab".

Second way:
Choose suffix from index = 4, so resulting s = "ababab".

Constraints:

 * 2 <= s.length <= 5 * 105
 * 1 <= k <= 1015
 * s.length == t.length
 * s and t consist of only lowercase English alphabets.

Please complete the code below to solve above prblem:
```python
class Solution:
    def numberOfWays(self, s: str, t: str, k: int) -> int:

```

my_solution = Solution()

test_input = { "s": "abcd", "t": "cdab", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 2

test_input = { "s": "ababab", "t": "ababab", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 2

test_input = { "s": "goxoq", "t": "dfqgl", "k": 244326024901249 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "ceoceo", "t": "eoceoc", "k": 4 }
assert my_solution.numberOfWays(**test_input) == 208

test_input = { "s": "ib", "t": "ib", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "ttttttt", "t": "ttttttt", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 7776

test_input = { "s": "aaaa", "t": "aaaa", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 6561

test_input = { "s": "meplrmeplr", "t": "eplrmeplrm", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 956594

test_input = { "s": "dsmn", "t": "smnd", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 7

test_input = { "s": "jjj", "t": "jjj", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 1024

test_input = { "s": "rrrrr", "t": "rrrrr", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 4

test_input = { "s": "fefe", "t": "fefe", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 9841

test_input = { "s": "pfly", "t": "wvqr", "k": 840550364246523 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "ltjwwltjww", "t": "jwwltjwwlt", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 2

test_input = { "s": "mb", "t": "mb", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "jjjjjjjjjj", "t": "jjjjjjjjjj", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 729

test_input = { "s": "oqytlmi", "t": "lmioqyt", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 239945

test_input = { "s": "hpcg", "t": "pcgh", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 61

test_input = { "s": "bqbqbqbqbq", "t": "bqbqbqbqbq", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 193710244

test_input = { "s": "ccccccccc", "t": "ccccccccc", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 2097152

test_input = { "s": "jjjjjjjjjj", "t": "jjjjjjjjjj", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 387420489

test_input = { "s": "qqqq", "t": "qqqq", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 19683

test_input = { "s": "loppaqg", "t": "nvbxtmh", "k": 104865546226045 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "qqqqqqqqqq", "t": "qqqqqqqqqq", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 729

test_input = { "s": "qsqsqsqsqs", "t": "qsqsqsqsqs", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 41

test_input = { "s": "nnnnn", "t": "nnnnn", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 1024

test_input = { "s": "klncccd", "t": "klncccd", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "qqqqq", "t": "qqqqq", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 262144

test_input = { "s": "qvxrlh", "t": "hqvxrl", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 2604

test_input = { "s": "uuuu", "t": "uuuu", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 19683

test_input = { "s": "sss", "t": "sss", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 128

test_input = { "s": "gggggggggg", "t": "gggggggggg", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 9

test_input = { "s": "ks", "t": "cj", "k": 400700574233583 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "lllllllll", "t": "lllllllll", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 32768

test_input = { "s": "uhixx", "t": "xxuhi", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 13

test_input = { "s": "vkrvkrvkr", "t": "rvkrvkrvk", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 21

test_input = { "s": "xtxtxtxt", "t": "xtxtxtxt", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 2882401

test_input = { "s": "nzybrhi", "t": "rhinzyb", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 6665

test_input = { "s": "ff", "t": "ff", "k": 4 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "ubagdasws", "t": "aswsubagd", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 14913081

test_input = { "s": "aaaaa", "t": "aaaaa", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 1048576

test_input = { "s": "iiiiiiiiii", "t": "iiiiiiiiii", "k": 4 }
assert my_solution.numberOfWays(**test_input) == 6561

test_input = { "s": "nnjqjmgome", "t": "gbfuecwlqc", "k": 359221508193514 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "slmzyj", "t": "slmzyj", "k": 4 }
assert my_solution.numberOfWays(**test_input) == 105

test_input = { "s": "vfyxl", "t": "vfyxl", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 209716

test_input = { "s": "sxzfvsxzfv", "t": "vsxzfvsxzf", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 16

test_input = { "s": "kalt", "t": "ltka", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 547

test_input = { "s": "jj", "t": "jj", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "bcriunp", "t": "criunpb", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 5

test_input = { "s": "rutmzyj", "t": "zyjrutm", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 6665

test_input = { "s": "vvvvv", "t": "vvvvv", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 64

test_input = { "s": "hlld", "t": "hlld", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 4920

test_input = { "s": "kctcsgswa", "t": "qfyyjeohe", "k": 966836940319300 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "otwqxmpktt", "t": "totwqxmpkt", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 478297

test_input = { "s": "kkkkkkk", "t": "kkkkkkk", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 279936

test_input = { "s": "iyl", "t": "iyl", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 22

test_input = { "s": "glao", "t": "ogla", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 14762

test_input = { "s": "jp", "t": "jp", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "uuuuuu", "t": "uuuuuu", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 78125

test_input = { "s": "achach", "t": "achach", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 3255209

test_input = { "s": "uuuuuuuu", "t": "uuuuuuuu", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 823543

test_input = { "s": "gjh", "t": "jhg", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 171

test_input = { "s": "cliuw", "t": "fphcn", "k": 647756904366432 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "zmcum", "t": "mzmcu", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "ll", "t": "ll", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "ccccc", "t": "ccccc", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 4

test_input = { "s": "rrrr", "t": "rrrr", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 3

test_input = { "s": "ih", "t": "hi", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "qfgihqrw", "t": "rwqfgihq", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 720600

test_input = { "s": "cd", "t": "cd", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "oooooooooo", "t": "oooooooooo", "k": 4 }
assert my_solution.numberOfWays(**test_input) == 6561

test_input = { "s": "wp", "t": "wp", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "rqq", "t": "nln", "k": 776508964349618 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "rr", "t": "rr", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "knwppsd", "t": "psdknwp", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 5

test_input = { "s": "epfeepfe", "t": "feepfeep", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 10088402

test_input = { "s": "wwwww", "t": "wwwww", "k": 9 }
assert my_solution.numberOfWays(**test_input) == 262144

test_input = { "s": "cdcdcdcd", "t": "cdcdcdcd", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 58825

test_input = { "s": "uphfr", "t": "fruph", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 3277

test_input = { "s": "cocococo", "t": "cocococo", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 171

test_input = { "s": "vhzjo", "t": "jovhz", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "bbbbbbbbbb", "t": "bbbbbbbbbb", "k": 1 }
assert my_solution.numberOfWays(**test_input) == 9

test_input = { "s": "pgnrstuh", "t": "yjzhldlg", "k": 618648276258027 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "cccccc", "t": "cccccc", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 3125

test_input = { "s": "kkkkkkk", "t": "kkkkkkk", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 216

test_input = { "s": "lxqqzsvej", "t": "svejlxqqz", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 57

test_input = { "s": "lllll", "t": "lllll", "k": 3 }
assert my_solution.numberOfWays(**test_input) == 64

test_input = { "s": "hhhhhhhhhh", "t": "hhhhhhhhhh", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 43046721

test_input = { "s": "gggg", "t": "gggg", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 243

test_input = { "s": "jj", "t": "jj", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "uuuuuuuuu", "t": "uuuuuuuuu", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 73741817

test_input = { "s": "qvx", "t": "vxq", "k": 8 }
assert my_solution.numberOfWays(**test_input) == 85

test_input = { "s": "nolnqlgqcs", "t": "jkguybcfcu", "k": 179216079747558 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "xpk", "t": "xpk", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 22

test_input = { "s": "xzoyb", "t": "bxzoy", "k": 5 }
assert my_solution.numberOfWays(**test_input) == 205

test_input = { "s": "krxjvvg", "t": "krxjvvg", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 6

test_input = { "s": "ks", "t": "sk", "k": 2 }
assert my_solution.numberOfWays(**test_input) == 0

test_input = { "s": "ty", "t": "ty", "k": 6 }
assert my_solution.numberOfWays(**test_input) == 1

test_input = { "s": "otototot", "t": "totototo", "k": 7 }
assert my_solution.numberOfWays(**test_input) == 411772

test_input = { "s": "uoaowbdznp", "t": "npuoaowbdz", "k": 10 }
assert my_solution.numberOfWays(**test_input) == 348678440


count-symmetric-integers

Count Symmetric Integers

Prompt:
"""
You are given two positive integers low and high.

An integer x consisting of 2 * n digits is symmetric if the sum of the first n digits of x is equal to the sum of the last n digits of x. Numbers with an odd number of digits are never symmetric.

Return the number of symmetric integers in the range [low, high].

Example 1:

Input: low = 1, high = 100
Output: 9
Explanation: There are 9 symmetric integers between 1 and 100: 11, 22, 33, 44, 55, 66, 77, 88, and 99.

Example 2:

Input: low = 1200, high = 1230
Output: 4
Explanation: There are 4 symmetric integers between 1200 and 1230: 1203, 1212, 1221, and 1230.

Constraints:

 * 1 <= low <= high <= 104
"""
class Solution:
    def countSymmetricIntegers(self, low: int, high: int) -> int:

You are given two positive integers low and high.

An integer x consisting of 2 * n digits is symmetric if the sum of the first n digits of x is equal to the sum of the last n digits of x. Numbers with an odd number of digits are never symmetric.

Return the number of symmetric integers in the range [low, high].

Example 1:

Input: low = 1, high = 100
Output: 9
Explanation: There are 9 symmetric integers between 1 and 100: 11, 22, 33, 44, 55, 66, 77, 88, and 99.

Example 2:

Input: low = 1200, high = 1230
Output: 4
Explanation: There are 4 symmetric integers between 1200 and 1230: 1203, 1212, 1221, and 1230.

Constraints:

 * 1 <= low <= high <= 104

Please complete the code below to solve above prblem:
```python
class Solution:
    def countSymmetricIntegers(self, low: int, high: int) -> int:

```

my_solution = Solution()

test_input = { "low": 1, "high": 100 }
assert my_solution.countSymmetricIntegers(**test_input) == 9

test_input = { "low": 1200, "high": 1230 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 1 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 2 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 3 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 4 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 5 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 6 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 7 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 8 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 9 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 10 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 1, "high": 11 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 12 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 13 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 14 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 15 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 16 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 17 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 18 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 19 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 20 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 21 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 1, "high": 22 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 23 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 24 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 25 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 26 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 27 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 28 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 29 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 30 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 31 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 32 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 1, "high": 33 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 34 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 35 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 36 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 37 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 38 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 39 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 40 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 41 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 42 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 43 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 1, "high": 44 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 45 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 46 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 47 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 48 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 100, "high": 1782 }
assert my_solution.countSymmetricIntegers(**test_input) == 44

test_input = { "low": 1, "high": 49 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 50 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 51 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 52 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 53 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 54 }
assert my_solution.countSymmetricIntegers(**test_input) == 4

test_input = { "low": 1, "high": 55 }
assert my_solution.countSymmetricIntegers(**test_input) == 5

test_input = { "low": 1, "high": 56 }
assert my_solution.countSymmetricIntegers(**test_input) == 5

test_input = { "low": 1, "high": 57 }
assert my_solution.countSymmetricIntegers(**test_input) == 5

test_input = { "low": 1, "high": 58 }
assert my_solution.countSymmetricIntegers(**test_input) == 5

test_input = { "low": 1, "high": 59 }
assert my_solution.countSymmetricIntegers(**test_input) == 5

test_input = { "low": 1, "high": 60 }
assert my_solution.countSymmetricIntegers(**test_input) == 5

test_input = { "low": 2, "high": 2 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 3 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 4 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 5 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 6 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 7 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 8 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 9 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 10 }
assert my_solution.countSymmetricIntegers(**test_input) == 0

test_input = { "low": 2, "high": 11 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 12 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 13 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 14 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 15 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 16 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 17 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 18 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 19 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 20 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 21 }
assert my_solution.countSymmetricIntegers(**test_input) == 1

test_input = { "low": 2, "high": 22 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 23 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 24 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 25 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 26 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 27 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 28 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 29 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 30 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 31 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 32 }
assert my_solution.countSymmetricIntegers(**test_input) == 2

test_input = { "low": 2, "high": 33 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 2, "high": 34 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 2, "high": 35 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 2, "high": 36 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 2, "high": 37 }
assert my_solution.countSymmetricIntegers(**test_input) == 3

test_input = { "low": 2, "high": 38 }
assert my_solution.countSymmetricIntegers(**test_input) == 3