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

PROBLEM:
You are given an integer n and a 2D integer array queries.
There are n cities numbered from 0 to n - 1. Initially, there is a unidirectional road from city i to city i + 1 for all 0 <= i < n - 1.
queries[i] = [ui, vi] represents the addition of a new unidirectional road from city ui to city vi. After each query, you need to find the length of the shortest path from city 0 to city n - 1.
Return an array answer where for each i in the range [0, queries.length - 1], answer[i] is the length of the shortest path from city 0 to city n - 1 after processing the first i + 1 queries.

Example 1:

Input: n = 5, queries = [[2,4],[0,2],[0,4]]
Output: [3,2,1]
Explanation:

After the addition of the road from 2 to 4, the length of the shortest path from 0 to 4 is 3.

After the addition of the road from 0 to 2, the length of the shortest path from 0 to 4 is 2.

After the addition of the road from 0 to 4, the length of the shortest path from 0 to 4 is 1.

Example 2:

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

After the addition of the road from 0 to 3, the length of the shortest path from 0 to 3 is 1.

After the addition of the road from 0 to 2, the length of the shortest path remains 1.

Constraints:

3 <= n <= 500
1 <= queries.length <= 500
queries[i].length == 2
0 <= queries[i][0] < queries[i][1] < n
1 < queries[i][1] - queries[i][0]
There are no repeated roads among the queries.

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

SOLUTION:

Question:
PROBLEM:
You are given an integer n and a 2D integer array queries.
There are n cities numbered from 0 to n - 1. Initially, there is a unidirectional road from city i to city i + 1 for all 0 <= i < n - 1.
queries[i] = [ui, vi] represents the addition of a new unidirectional road from city ui to city vi. After each query, you need to find the length of the shortest path from city 0 to city n - 1.
Return an array answer where for each i in the range [0, queries.length - 1], answer[i] is the length of the shortest path from city 0 to city n - 1 after processing the first i + 1 queries.

Example 1:

Input: n = 5, queries = [[2,4],[0,2],[0,4]]
Output: [3,2,1]
Explanation:

After the addition of the road from 2 to 4, the length of the shortest path from 0 to 4 is 3.

After the addition of the road from 0 to 2, the length of the shortest path from 0 to 4 is 2.

After the addition of the road from 0 to 4, the length of the shortest path from 0 to 4 is 1.

Example 2:

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

After the addition of the road from 0 to 3, the length of the shortest path from 0 to 3 is 1.

After the addition of the road from 0 to 2, the length of the shortest path remains 1.

Constraints:

3 <= n <= 500
1 <= queries.length <= 500
queries[i].length == 2
0 <= queries[i][0] < queries[i][1] < n
1 < queries[i][1] - queries[i][0]
There are no repeated roads among the queries.

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

SOLUTION:

assert Solution().shortestDistanceAfterQueries(n = 7, queries = [[0,5],[1,6],[2,4]]) == [2, 2, 2]

assert Solution().shortestDistanceAfterQueries(n = 6, queries = [[1,3],[2,5],[0,3]]) == [4, 3, 3]

assert Solution().shortestDistanceAfterQueries(n = 8, queries = [[0,6],[1,7],[2,5],[3,4]]) == [2, 2, 2, 2]

assert Solution().shortestDistanceAfterQueries(n = 7, queries = [[1,5],[2,6],[3,5]]) == [3, 3, 3]

assert Solution().shortestDistanceAfterQueries(n = 6, queries = [[1,3],[2,4],[0,3]]) == [4, 4, 3]

assert Solution().shortestDistanceAfterQueries(n = 6, queries = [[1,3],[2,5],[0,1],[3,4]]) == [4, 3, 3, 3]

assert Solution().shortestDistanceAfterQueries(n = 5, queries = [[2,4],[0,2],[0,4]]) == [3, 2, 1]

assert Solution().shortestDistanceAfterQueries(n = 4, queries = [[0,3],[0,2]]) == [1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 7, queries = [[0,5],[1,6],[2,4]]) == [2, 2, 2]

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

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 7, queries = [[1,5],[2,6],[3,5]]) == [3, 3, 3]

Answer: assert Solution().shortestDistanceAfterQueries(n = 6, queries = [[1,3],[2,4],[0,3]]) == [4, 4, 3]

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

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

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 50, queries = [[0,49],[0,48],[1,47],[2,46],[3,45],[4,44],[5,43],[6,42],[7,41],[8,40],[9,39],[10,38],[11,37],[12,36],[13,35],[14,34],[15,33],[16,32],[17,31],[18,30],[19,29],[20,28],[21,27],[22,26],[23,25]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 50, queries = [[0,25],[0,30],[0,35],[0,40],[0,45],[5,15],[5,20],[5,25],[5,30],[5,35],[5,40],[5,45],[10,20],[10,25],[10,30],[10,35],[10,40],[10,45],[15,25],[15,30],[15,35],[15,40],[15,45],[20,30],[20,35],[20,40],[20,45],[25,35],[25,40],[25,45],[30,40],[30,45],[35,45]]) == [25, 20, 15, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

Answer: assert Solution().shortestDistanceAfterQueries(n = 45, queries = [[0,18],[5,28],[10,34],[15,39],[20,41],[25,43],[30,44],[35,42],[1,19],[6,30],[11,35],[16,40],[21,42],[26,36],[31,37]]) == [27, 22, 21, 21, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]

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

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

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

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 50, queries = [[0,49],[1,48],[2,47],[3,46],[4,45],[5,44],[6,43],[7,42],[8,41],[9,40],[10,39],[11,38],[12,37],[13,36],[14,35],[15,34],[16,33],[17,32],[18,31],[19,30],[0,47],[2,45],[4,43],[6,41],[8,39],[10,38],[12,37],[14,36],[16,35],[18,34],[20,33],[22,32],[24,31],[26,30],[28,29]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 50, queries = [[0,49],[1,48],[2,47],[3,46],[4,45],[5,44],[6,43],[7,42],[8,41],[9,40],[10,39],[11,38],[12,37],[13,36],[14,35],[15,34],[16,33],[17,32],[18,31],[19,30],[20,29],[21,28],[22,27],[23,26],[24,25],[25,24],[26,23],[27,22],[28,21],[29,20],[30,19],[31,18],[32,17],[33,16],[34,15],[35,14],[36,13],[37,12],[38,11],[39,10],[40,9],[41,8],[42,7],[43,6],[44,5],[45,4],[46,3],[47,2],[48,1]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 30, queries = [[0,10],[0,15],[0,20],[5,25],[5,29],[10,19],[10,24],[15,23],[15,28],[20,22],[20,27],[25,26]]) == [20, 15, 10, 10, 6, 6, 6, 6, 3, 3, 3, 3]

Answer: assert Solution().shortestDistanceAfterQueries(n = 100, queries = [[0,99],[0,98],[1,97],[2,96],[3,95],[4,94],[5,93],[6,92],[7,91],[8,90],[9,89],[10,88],[11,87],[12,86],[13,85],[14,84],[15,83],[16,82],[17,81],[18,80],[19,79],[20,78],[21,77],[22,76],[23,75],[24,74],[25,73],[26,72],[27,71],[28,70],[29,69],[30,68],[31,67],[32,66],[33,65],[34,64],[35,63],[36,62],[37,61],[38,60],[39,59],[40,58],[41,57],[42,56],[43,55],[44,54],[45,53],[46,52],[47,51],[48,50]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 30, queries = [[0,20],[1,21],[2,22],[3,23],[4,24],[5,25],[6,26],[7,27],[8,28],[9,29],[10,25],[11,26],[12,27],[13,28],[14,29],[15,28],[16,29],[0,15],[2,21],[4,23],[6,25],[8,27]]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 3, 3, 3, 3, 3]

Answer: assert Solution().shortestDistanceAfterQueries(n = 15, queries = [[0,10],[1,11],[2,12],[3,13],[4,14],[5,13],[6,14],[0,9],[2,11],[4,12]]) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 12, queries = [[0,6],[2,8],[3,9],[5,10],[7,11],[1,5]]) == [6, 6, 6, 6, 3, 3]

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 40, queries = [[0,15],[5,25],[10,30],[15,35],[20,37],[25,38],[30,39],[1,16],[6,26],[11,31],[16,36],[21,32],[26,33]]) == [25, 20, 20, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 15, queries = [[0,14],[1,10],[2,8],[3,9],[4,11],[5,12],[6,13]]) == [1, 1, 1, 1, 1, 1, 1]

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

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

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 15, queries = [[0,14],[0,7],[1,12],[2,11],[3,10],[4,9],[5,8],[6,7]]) == [1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 30, queries = [[0,25],[1,26],[2,27],[3,28],[4,29],[5,15],[6,16],[7,17],[8,18],[9,19],[10,20],[11,21],[12,22],[13,23],[14,24]]) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,15],[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,20],[11,21],[12,22],[13,23],[14,24]]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]

Answer: assert Solution().shortestDistanceAfterQueries(n = 30, queries = [[0,12],[5,18],[10,22],[15,24],[20,28],[25,29],[1,13],[6,19],[11,23],[16,25]]) == [18, 17, 17, 10, 10, 7, 7, 7, 7, 7]

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 30, queries = [[0,29],[1,28],[2,27],[3,26],[4,25],[5,24],[6,23],[7,22],[8,21],[9,20],[10,19],[11,18],[12,17],[13,16],[14,15],[15,14],[16,13],[17,12],[18,11],[19,10],[20,9],[21,8],[22,7],[23,6],[24,5],[25,4],[26,3],[27,2],[28,1]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 15, queries = [[0,14],[1,13],[2,12],[3,11],[4,10],[5,9],[6,8]]) == [1, 1, 1, 1, 1, 1, 1]

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 40, queries = [[0,10],[0,15],[0,20],[0,25],[0,30],[5,15],[5,20],[5,25],[5,30],[10,20],[10,25],[10,30],[15,25],[15,30],[20,30]]) == [30, 25, 20, 15, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]

Answer: assert Solution().shortestDistanceAfterQueries(n = 40, queries = [[0,35],[1,36],[2,37],[3,38],[4,39],[5,25],[6,26],[7,27],[8,28],[9,29],[10,30],[11,31],[12,32],[13,33],[14,34],[15,20],[16,21],[17,22],[18,23],[19,24]]) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

Answer: assert Solution().shortestDistanceAfterQueries(n = 50, queries = [[0,45],[1,46],[2,47],[3,48],[4,49],[5,35],[6,36],[7,37],[8,38],[9,39],[10,40],[11,41],[12,42],[13,43],[14,44],[15,30],[16,31],[17,32],[18,33],[19,34],[20,25],[21,26],[22,27],[23,28],[24,29]]) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

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

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

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,24],[0,23],[0,22],[1,21],[2,20],[3,19],[4,18],[5,17],[6,16],[7,15],[8,14],[9,13],[10,12]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 15, queries = [[0,4],[1,8],[2,10],[3,11],[4,12],[5,13],[6,14],[0,13],[1,14]]) == [11, 8, 7, 7, 4, 4, 4, 2, 2]

Answer: assert Solution().shortestDistanceAfterQueries(n = 20, queries = [[0,15],[5,18],[10,19],[1,12],[3,17],[7,16],[9,14],[2,13]]) == [5, 5, 5, 5, 5, 5, 5, 5]

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 30, queries = [[0,29],[1,28],[2,27],[3,26],[4,25],[5,24],[6,23],[7,22],[8,21],[9,20],[10,19],[11,18],[12,17],[13,16],[14,15],[0,27],[2,25],[4,23],[6,21],[8,19],[10,18],[12,17],[14,16]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,24],[1,23],[2,22],[3,21],[4,20],[5,19],[6,18],[7,17],[8,16],[9,15],[10,14],[11,13],[12,12],[13,11],[14,10],[15,9],[16,8],[17,7],[18,6],[19,5],[20,4],[21,3],[22,2],[23,1]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,15],[1,8],[2,10],[3,12],[4,14],[5,16],[6,18],[7,20],[8,22],[9,24],[10,17],[11,19],[12,21],[13,23]]) == [10, 10, 10, 10, 10, 10, 10, 10, 5, 4, 4, 4, 4, 4]

Answer: assert Solution().shortestDistanceAfterQueries(n = 18, queries = [[0,17],[0,9],[1,16],[2,15],[3,14],[4,13],[5,12],[6,11],[7,10],[8,9]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 35, queries = [[0,13],[5,20],[10,24],[15,28],[20,32],[25,34],[30,33],[1,14],[6,21],[11,25],[16,29],[21,31]]) == [22, 20, 20, 10, 9, 9, 8, 8, 8, 8, 8, 8]

Answer: assert Solution().shortestDistanceAfterQueries(n = 15, queries = [[0,14],[0,13],[0,12],[1,11],[2,10],[3,9],[4,8],[5,7]]) == [1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,10],[5,20],[10,22],[15,23],[20,24],[2,12],[7,17],[12,21]]) == [15, 10, 4, 4, 4, 4, 4, 4]

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

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

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,15],[1,16],[2,17],[3,18],[4,19],[5,20],[6,21],[7,22],[8,23],[9,24],[10,18],[11,19],[12,20],[13,21],[14,22],[0,8],[2,16],[4,18],[6,20],[8,22]]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 3, 3, 3, 3, 3]

Answer: assert Solution().shortestDistanceAfterQueries(n = 50, queries = [[0,20],[5,30],[10,36],[15,40],[20,44],[25,47],[30,48],[35,49],[40,46],[1,21],[6,31],[11,37],[16,41],[21,43],[26,38],[31,39],[36,45]]) == [30, 25, 24, 24, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]

Answer: assert Solution().shortestDistanceAfterQueries(n = 25, queries = [[0,24],[0,13],[1,23],[2,22],[3,21],[4,20],[5,19],[6,18],[7,17],[8,16],[9,15],[10,14],[11,12]]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Answer: assert Solution().shortestDistanceAfterQueries(n = 20, queries = [[0,10],[1,5],[2,8],[3,7],[4,6],[5,15],[6,12],[7,18],[8,16],[9,19]]) == [10, 10, 10, 10, 10, 7, 7, 6, 6, 5]

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
    def shortestDistanceAfterQueries(
        self, n: int, queries: List[List[int]]
    ) -> List[int]:
        def bfs(i: int) -> int:
            q = deque([i])
            vis = [False] * n
            vis[i] = True
            d = 0
            while 1:
                for _ in range(len(q)):
                    u = q.popleft()
                    if u == n - 1:
                        return d
                    for v in g[u]:
                        if not vis[v]:
                            vis[v] = True
                            q.append(v)
                d += 1

        g = [[i + 1] for i in range(n - 1)]
        ans = []
        for u, v in queries:
            g[u].append(v)
            ans.append(bfs(0))
        return ans


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

PROBLEM:
There is an undirected tree with n nodes labeled from 0 to n - 1, and rooted at node 0. You are given a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.
A node is good if all the subtrees rooted at its children have the same size.
Return the number of good nodes in the given tree.
A subtree of treeName is a tree consisting of a node in treeName and all of its descendants.

Example 1:

Input: edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]
Output: 7
Explanation:

All of the nodes of the given tree are good.

Example 2:

Input: edges = [[0,1],[1,2],[2,3],[3,4],[0,5],[1,6],[2,7],[3,8]]
Output: 6
Explanation:

There are 6 good nodes in the given tree. They are colored in the image above.
Example 3:

Input: edges = [[0,1],[1,2],[1,3],[1,4],[0,5],[5,6],[6,7],[7,8],[0,9],[9,10],[9,12],[10,11]]
Output: 12
Explanation:

All nodes except node 9 are good.

Constraints:

2 <= n <= 105
edges.length == n - 1
edges[i].length == 2
0 <= ai, bi < n
The input is generated such that edges represents a valid tree.

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

SOLUTION:

Question:
PROBLEM:
There is an undirected tree with n nodes labeled from 0 to n - 1, and rooted at node 0. You are given a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.
A node is good if all the subtrees rooted at its children have the same size.
Return the number of good nodes in the given tree.
A subtree of treeName is a tree consisting of a node in treeName and all of its descendants.

Example 1:

Input: edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]
Output: 7
Explanation:

All of the nodes of the given tree are good.

Example 2:

Input: edges = [[0,1],[1,2],[2,3],[3,4],[0,5],[1,6],[2,7],[3,8]]
Output: 6
Explanation:

There are 6 good nodes in the given tree. They are colored in the image above.
Example 3:

Input: edges = [[0,1],[1,2],[1,3],[1,4],[0,5],[5,6],[6,7],[7,8],[0,9],[9,10],[9,12],[10,11]]
Output: 12
Explanation:

All nodes except node 9 are good.

Constraints:

2 <= n <= 105
edges.length == n - 1
edges[i].length == 2
0 <= ai, bi < n
The input is generated such that edges represents a valid tree.

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

SOLUTION:

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

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

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]) == 7

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[1,3],[2,4],[2,5],[3,6],[3,7],[4,8],[4,9],[5,10],[5,11],[6,12],[6,13],[7,14],[7,15],[8,16],[8,17],[9,18],[9,19],[10,20],[10,21],[11,22],[11,23],[12,24],[12,25],[13,26],[13,27],[14,28],[14,29]]) == 27

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22],[11,23],[11,24],[12,25],[12,26],[13,27],[13,28],[14,29],[14,30]]) == 31

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[0,3],[1,4],[1,5],[1,6],[2,7],[2,8],[2,9],[3,10],[3,11],[3,12],[4,13],[4,14],[5,15],[5,16],[6,17],[6,18],[6,19],[7,20],[7,21],[8,22],[8,23],[9,24],[9,25],[10,26],[10,27],[11,28],[11,29],[12,30],[12,31]]) == 30

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

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[1,3],[2,4],[2,5],[3,6],[3,7],[4,8],[4,9],[5,10],[5,11],[6,12],[6,13],[7,14],[7,15],[8,16],[8,17],[9,18],[9,19],[10,20],[10,21],[11,22],[11,23],[12,24],[12,25],[13,26],[13,27]]) == 26

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[0,3],[1,4],[1,5],[1,6],[2,7],[2,8],[2,9],[3,10],[3,11],[3,12],[4,13],[4,14],[5,15],[5,16],[6,17],[6,18],[7,19],[7,20],[8,21],[8,22],[9,23],[9,24]]) == 24

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26],[26,27],[27,28],[28,29]]) == 30

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[1,3],[2,4],[2,5],[3,6],[3,7],[4,8],[4,9],[5,10],[5,11],[6,12],[6,13],[7,14],[7,15],[8,16],[8,17],[9,18],[9,19],[10,20],[10,21],[11,22],[11,23]]) == 23

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[1,5],[2,6],[2,7],[2,8],[6,9],[6,10],[7,11],[7,12],[8,13],[8,14],[1,15],[15,16],[15,17]]) == 16

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

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[0,3],[0,4],[0,5],[1,6],[1,7],[2,8],[2,9],[3,10],[3,11],[4,12],[4,13],[5,14],[5,15],[6,16],[6,17],[7,18],[7,19],[8,20],[8,21],[9,22],[9,23],[10,24],[10,25],[11,26],[11,27],[12,28],[12,29],[13,30],[13,31],[14,32],[14,33]]) == 32

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[8,16],[8,17],[9,18],[10,19],[10,20],[11,21],[11,22],[12,23],[12,24]]) == 21

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

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

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[3,9],[4,10],[4,11],[5,12],[5,13],[6,14],[6,15],[7,16],[7,17],[7,18],[8,19],[8,20],[8,21],[9,22],[9,23],[10,24],[10,25],[11,26],[11,27],[12,28],[12,29],[13,30],[13,31],[14,32],[14,33]]) == 30

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[3,9],[4,10],[4,11],[5,12],[5,13],[5,14],[6,15],[6,16],[6,17]]) == 16

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[2,7],[3,8],[3,9],[3,10],[4,11],[4,12],[5,13],[5,14],[6,15],[6,16],[7,17],[7,18],[7,19],[8,20],[8,21],[8,22],[9,23],[9,24],[9,25],[10,26],[10,27],[10,28],[11,29],[11,30],[11,31]]) == 28

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[0,3],[0,4],[1,5],[1,6],[2,7],[2,8],[3,9],[3,10],[4,11],[4,12],[5,13],[5,14],[6,15],[6,16],[7,17],[7,18],[8,19],[8,20],[9,21],[9,22],[10,23],[10,24],[11,25],[11,26],[12,27],[12,28]]) == 29

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22],[11,23],[11,24],[12,25],[12,26]]) == 25

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14],[7,15],[7,16],[8,17],[8,18],[9,19],[9,20],[10,21],[10,22]]) == 23

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

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

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

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

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[0,3],[1,4],[1,5],[2,6],[2,7],[3,8],[3,9],[4,10],[4,11],[5,12],[5,13],[6,14],[6,15],[7,16],[7,17],[8,18],[8,19],[9,20],[9,21]]) == 22

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[1,3],[1,4],[1,5],[2,6],[2,7],[3,8],[3,9],[4,10],[4,11],[5,12],[5,13],[6,14],[6,15],[7,16],[7,17]]) == 17

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

Answer: assert Solution().countGoodNodes(edges = [[0,1],[1,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[4,11],[5,12],[5,13],[6,14],[6,15],[7,16],[7,17],[8,18],[8,19],[9,20],[9,21],[10,22],[10,23],[11,24],[11,25]]) == 25

Answer: assert Solution().countGoodNodes(edges = [[0,1],[0,2],[0,3],[1,4],[2,5],[3,6],[4,7],[4,8],[4,9],[5,10],[5,11],[6,12],[7,13],[7,14],[8,15],[8,16],[9,17],[10,18],[10,19],[11,20],[11,21]]) == 20

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
    def countGoodNodes(self, edges: List[List[int]]) -> int:
        def dfs(a: int, fa: int) -> int:
            pre = -1
            cnt = ok = 1
            for b in g[a]:
                if b != fa:
                    cur = dfs(b, a)
                    cnt += cur
                    if pre < 0:
                        pre = cur
                    elif pre != cur:
                        ok = 0
            nonlocal ans
            ans += ok
            return cnt

        g = defaultdict(list)
        for a, b in edges:
            g[a].append(b)
            g[b].append(a)
        ans = 0
        dfs(0, -1)
        return ans


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

PROBLEM:
You are given an array of positive integers nums of length n.
We call a pair of non-negative integer arrays (arr1, arr2) monotonic if:

The lengths of both arrays are n.
arr1 is monotonically non-decreasing, in other words, arr1[0] <= arr1[1] <= ... <= arr1[n - 1].
arr2 is monotonically non-increasing, in other words, arr2[0] >= arr2[1] >= ... >= arr2[n - 1].
arr1[i] + arr2[i] == nums[i] for all 0 <= i <= n - 1.

Return the count of monotonic pairs.
Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: nums = [2,3,2]
Output: 4
Explanation:
The good pairs are:

([0, 1, 1], [2, 2, 1])
([0, 1, 2], [2, 2, 0])
([0, 2, 2], [2, 1, 0])
([1, 2, 2], [1, 1, 0])

Example 2:

Input: nums = [5,5,5,5]
Output: 126

Constraints:

1 <= n == nums.length <= 2000
1 <= nums[i] <= 50

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

SOLUTION:

Question:
PROBLEM:
You are given an array of positive integers nums of length n.
We call a pair of non-negative integer arrays (arr1, arr2) monotonic if:

The lengths of both arrays are n.
arr1 is monotonically non-decreasing, in other words, arr1[0] <= arr1[1] <= ... <= arr1[n - 1].
arr2 is monotonically non-increasing, in other words, arr2[0] >= arr2[1] >= ... >= arr2[n - 1].
arr1[i] + arr2[i] == nums[i] for all 0 <= i <= n - 1.

Return the count of monotonic pairs.
Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: nums = [2,3,2]
Output: 4
Explanation:
The good pairs are:

([0, 1, 1], [2, 2, 1])
([0, 1, 2], [2, 2, 0])
([0, 2, 2], [2, 1, 0])
([1, 2, 2], [1, 1, 0])

Example 2:

Input: nums = [5,5,5,5]
Output: 126

Constraints:

1 <= n == nums.length <= 2000
1 <= nums[i] <= 50

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

SOLUTION:

assert Solution().countOfPairs(nums = [50,1,50,1,50]) == 0

assert Solution().countOfPairs(nums = [3,3,3,3,3,3]) == 84

assert Solution().countOfPairs(nums = [10,20,30,40,50]) == 3003

assert Solution().countOfPairs(nums = [5,5,5,5]) == 126

assert Solution().countOfPairs(nums = [1,2,3,4,5]) == 6

assert Solution().countOfPairs(nums = [10,9,8,7,6]) == 462

assert Solution().countOfPairs(nums = [2,3,2]) == 4

assert Solution().countOfPairs(nums = [10,10,10]) == 286

assert Solution().countOfPairs(nums = [1,1,1,1,1]) == 6

assert Solution().countOfPairs(nums = [25,25,25,25,25]) == 142506

assert Solution().countOfPairs(nums = [1,2,1,2,1,2]) == 0

assert Solution().countOfPairs(nums = [3,2,1]) == 4

assert Solution().countOfPairs(nums = [5,4,3,2,1]) == 6

assert Solution().countOfPairs(nums = [3,2,1,2,3]) == 6

assert Solution().countOfPairs(nums = [1,2,3]) == 4

assert Solution().countOfPairs(nums = [50,40,30,20,10]) == 3003

assert Solution().countOfPairs(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5]) == 0

assert Solution().countOfPairs(nums = [10, 20, 15, 25, 30]) == 252

assert Solution().countOfPairs(nums = [4, 5, 3, 6, 2]) == 0

assert Solution().countOfPairs(nums = [10, 15, 10, 5, 20]) == 1

assert Solution().countOfPairs(nums = [1, 5, 1, 5, 1, 5, 1, 5, 1, 5]) == 0

assert Solution().countOfPairs(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7]) == 0

assert Solution().countOfPairs(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1]) == 0

assert Solution().countOfPairs(nums = [5, 4, 3, 2, 1]) == 6

assert Solution().countOfPairs(nums = [3, 4, 3, 5, 2, 4, 3, 5, 2, 4]) == 0

assert Solution().countOfPairs(nums = [10, 20, 30, 40, 50]) == 3003

assert Solution().countOfPairs(nums = [5, 3, 6, 7, 4, 3]) == 0

assert Solution().countOfPairs(nums = [30, 20, 10, 0, 10, 20, 30]) == 1

Answer: assert Solution().countOfPairs(nums = [50,1,50,1,50]) == 0

Answer: assert Solution().countOfPairs(nums = [3,3,3,3,3,3]) == 84

Answer: assert Solution().countOfPairs(nums = [10,20,30,40,50]) == 3003

Answer: assert Solution().countOfPairs(nums = [5,5,5,5]) == 126

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

Answer: assert Solution().countOfPairs(nums = [10,9,8,7,6]) == 462

Answer: assert Solution().countOfPairs(nums = [2,3,2]) == 4

Answer: assert Solution().countOfPairs(nums = [10,10,10]) == 286

Answer: assert Solution().countOfPairs(nums = [1,1,1,1,1,1,1,1,1,1]) == 11

Answer: assert Solution().countOfPairs(nums = [1,1,1,1,1]) == 6

Answer: assert Solution().countOfPairs(nums = [25,25,25,25,25]) == 142506

Answer: assert Solution().countOfPairs(nums = [1,2,1,2,1,2]) == 0

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

Answer: assert Solution().countOfPairs(nums = [50,50,50,50,50,50]) == 32468436

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

Answer: assert Solution().countOfPairs(nums = [50,50,50,50,50,50,50,50,50,50]) == 394027041

Answer: assert Solution().countOfPairs(nums = [3,2,1,2,3]) == 6

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

Answer: assert Solution().countOfPairs(nums = [50,40,30,20,10]) == 3003

Answer: assert Solution().countOfPairs(nums = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15]) == 247943139

Answer: assert Solution().countOfPairs(nums = [15, 10, 15, 10, 15, 10, 15, 10, 15, 10]) == 0

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

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

Answer: assert Solution().countOfPairs(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5461512

Answer: assert Solution().countOfPairs(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 993396758

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

Answer: assert Solution().countOfPairs(nums = [10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == 21

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

Answer: assert Solution().countOfPairs(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 16

Answer: assert Solution().countOfPairs(nums = [10, 20, 15, 25, 30]) == 252

Answer: assert Solution().countOfPairs(nums = [45, 40, 35, 30, 25, 20, 15, 10, 5]) == 2002

Answer: assert Solution().countOfPairs(nums = [45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45]) == 348776183

Answer: assert Solution().countOfPairs(nums = [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30]) == 211914057

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

Answer: assert Solution().countOfPairs(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 888030

Answer: assert Solution().countOfPairs(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 286

Answer: assert Solution().countOfPairs(nums = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == 4845

Answer: assert Solution().countOfPairs(nums = [45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45]) == 463627631

Answer: assert Solution().countOfPairs(nums = [30, 30, 30, 30, 30, 30, 30, 30, 30, 30]) == 847660528

Answer: assert Solution().countOfPairs(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210

Answer: assert Solution().countOfPairs(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 52215702

Answer: assert Solution().countOfPairs(nums = [3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 21

Answer: assert Solution().countOfPairs(nums = [42, 23, 50, 17, 30, 28, 49, 35, 41, 26]) == 0

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

Answer: assert Solution().countOfPairs(nums = [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 1

Answer: assert Solution().countOfPairs(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 231

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

Answer: assert Solution().countOfPairs(nums = [10, 20, 30, 40, 50, 40, 30, 20, 10]) == 0

Answer: assert Solution().countOfPairs(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25]) == 225344776

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

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 26

Answer: assert Solution().countOfPairs(nums = [15, 20, 10, 25, 5, 30, 20, 15, 35, 25]) == 0

Answer: assert Solution().countOfPairs(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31]) == 155084415

Answer: assert Solution().countOfPairs(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 324632

Answer: assert Solution().countOfPairs(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 5456

Answer: assert Solution().countOfPairs(nums = [10, 15, 10, 5, 20]) == 1

Answer: assert Solution().countOfPairs(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55]) == 184756

Answer: assert Solution().countOfPairs(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25]) == 870807943

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

Answer: assert Solution().countOfPairs(nums = [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30]) == 493985381

Answer: assert Solution().countOfPairs(nums = [10, 20, 15, 10, 25, 30, 20, 15]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 5, 1, 5, 1, 5, 1, 5, 1, 5]) == 0

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

Answer: assert Solution().countOfPairs(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41]) == 777711786

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

Answer: assert Solution().countOfPairs(nums = [50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1]) == 0

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

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

Answer: assert Solution().countOfPairs(nums = [50, 49, 48, 47, 46, 45]) == 18009460

Answer: assert Solution().countOfPairs(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 30

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

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

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

Answer: assert Solution().countOfPairs(nums = [40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 40, 30, 20, 10, 0]) == 0

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

Answer: assert Solution().countOfPairs(nums = [42, 38, 42, 38, 42, 38, 42, 38, 42, 38, 42, 38, 42, 38, 42, 38, 42, 38, 42, 38]) == 231

Answer: assert Solution().countOfPairs(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 66

Answer: assert Solution().countOfPairs(nums = [10, 20, 30, 40, 50]) == 3003

Answer: assert Solution().countOfPairs(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 11480

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

Answer: assert Solution().countOfPairs(nums = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == 3876

Answer: assert Solution().countOfPairs(nums = [5, 3, 6, 7, 4, 3]) == 0

Answer: assert Solution().countOfPairs(nums = [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30]) == 737009364

Answer: assert Solution().countOfPairs(nums = [1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49]) == 14

Answer: assert Solution().countOfPairs(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 566153828

Answer: assert Solution().countOfPairs(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 0

Answer: assert Solution().countOfPairs(nums = [50, 25, 50, 25, 50, 25, 50, 25, 50, 25, 50, 25, 50, 25, 50, 25, 50, 25, 50, 25]) == 0

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

Answer: assert Solution().countOfPairs(nums = [2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]) == 0

Answer: assert Solution().countOfPairs(nums = [30, 20, 10, 0, 10, 20, 30]) == 1

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

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 50, 49, 47, 45, 43, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 0

Answer: assert Solution().countOfPairs(nums = [50, 50, 50, 50, 50, 50, 50, 50]) == 916797304

Answer: assert Solution().countOfPairs(nums = [25, 20, 15, 10, 5, 0, 5, 10, 15, 20, 25]) == 1

Answer: assert Solution().countOfPairs(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 113

Answer: assert Solution().countOfPairs(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 50, 49, 47, 43]) == 0

Answer: assert Solution().countOfPairs(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 1

Answer: assert Solution().countOfPairs(nums = [30, 20, 10, 5, 25, 15, 20, 10, 5]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 30, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 0

Answer: assert Solution().countOfPairs(nums = [30, 25, 20, 15, 10, 5, 10, 15, 20, 25, 30]) == 4368

Answer: assert Solution().countOfPairs(nums = [30, 20, 10, 30, 20, 10, 30, 20, 10, 30, 20, 10, 30, 20, 10, 30, 20, 10, 30, 20]) == 0

Answer: assert Solution().countOfPairs(nums = [42, 33, 24, 15, 6, 15, 24, 33, 42, 33, 24, 15, 6, 15, 24, 33, 42, 33, 24, 15]) == 0

Answer: assert Solution().countOfPairs(nums = [2, 3, 5, 7, 11, 13, 17, 19]) == 45

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
    def countOfPairs(self, nums: List[int]) -> int:
        mod = 10**9 + 7
        n, m = len(nums), max(nums)
        f = [[0] * (m + 1) for _ in range(n)]
        for j in range(nums[0] + 1):
            f[0][j] = 1
        for i in range(1, n):
            s = list(accumulate(f[i - 1]))
            for j in range(nums[i] + 1):
                k = min(j, j + nums[i - 1] - nums[i])
                if k >= 0:
                    f[i][j] = s[k] % mod
        return sum(f[-1][: nums[-1] + 1]) % mod


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

PROBLEM:
You are given an array of positive integers nums of length n.
We call a pair of non-negative integer arrays (arr1, arr2) monotonic if:

The lengths of both arrays are n.
arr1 is monotonically non-decreasing, in other words, arr1[0] <= arr1[1] <= ... <= arr1[n - 1].
arr2 is monotonically non-increasing, in other words, arr2[0] >= arr2[1] >= ... >= arr2[n - 1].
arr1[i] + arr2[i] == nums[i] for all 0 <= i <= n - 1.

Return the count of monotonic pairs.
Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: nums = [2,3,2]
Output: 4
Explanation:
The good pairs are:

([0, 1, 1], [2, 2, 1])
([0, 1, 2], [2, 2, 0])
([0, 2, 2], [2, 1, 0])
([1, 2, 2], [1, 1, 0])

Example 2:

Input: nums = [5,5,5,5]
Output: 126

Constraints:

1 <= n == nums.length <= 2000
1 <= nums[i] <= 1000

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

SOLUTION:

Question:
PROBLEM:
You are given an array of positive integers nums of length n.
We call a pair of non-negative integer arrays (arr1, arr2) monotonic if:

The lengths of both arrays are n.
arr1 is monotonically non-decreasing, in other words, arr1[0] <= arr1[1] <= ... <= arr1[n - 1].
arr2 is monotonically non-increasing, in other words, arr2[0] >= arr2[1] >= ... >= arr2[n - 1].
arr1[i] + arr2[i] == nums[i] for all 0 <= i <= n - 1.

Return the count of monotonic pairs.
Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: nums = [2,3,2]
Output: 4
Explanation:
The good pairs are:

([0, 1, 1], [2, 2, 1])
([0, 1, 2], [2, 2, 0])
([0, 2, 2], [2, 1, 0])
([1, 2, 2], [1, 1, 0])

Example 2:

Input: nums = [5,5,5,5]
Output: 126

Constraints:

1 <= n == nums.length <= 2000
1 <= nums[i] <= 1000

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

SOLUTION:

assert Solution().countOfPairs(nums = [2,3,2]) == 4

assert Solution().countOfPairs(nums = [1,2,1,2,1,2,1,2,1,2]) == 0

assert Solution().countOfPairs(nums = [1,1,1,1,1]) == 6

assert Solution().countOfPairs(nums = [5,4,3,2,1,2,3,4,5]) == 10

assert Solution().countOfPairs(nums = [5,5,5,5]) == 126

assert Solution().countOfPairs(nums = [1,2,3,4,5]) == 6

assert Solution().countOfPairs(nums = [10,9,8,7,6]) == 462

assert Solution().countOfPairs(nums = [1,1000,1,1000]) == 0

assert Solution().countOfPairs(nums = [3, 6, 9, 12, 15, 18, 21]) == 120

Answer: assert Solution().countOfPairs(nums = [2,3,2]) == 4

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

Answer: assert Solution().countOfPairs(nums = [1000,1000,1000,1000,1000,1000,1000,1000,1000,1000]) == 659632782

Answer: assert Solution().countOfPairs(nums = [1,1,1,1,1,1,1,1,1,1]) == 11

Answer: assert Solution().countOfPairs(nums = [1,2,1,2,1,2,1,2,1,2]) == 0

Answer: assert Solution().countOfPairs(nums = [1,1,1,1,1]) == 6

Answer: assert Solution().countOfPairs(nums = [10,20,30,40,50,40,30,20,10]) == 0

Answer: assert Solution().countOfPairs(nums = [3,3,3,3,3,3,3,3,3,3]) == 286

Answer: assert Solution().countOfPairs(nums = [5,4,3,2,1,2,3,4,5]) == 10

Answer: assert Solution().countOfPairs(nums = [5,5,5,5]) == 126

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

Answer: assert Solution().countOfPairs(nums = [10,9,8,7,6]) == 462

Answer: assert Solution().countOfPairs(nums = [1,1000,1,1000]) == 0

Answer: assert Solution().countOfPairs(nums = [1000,1000,1000]) == 167668501

Answer: assert Solution().countOfPairs(nums = [500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500]) == 379390517

Answer: assert Solution().countOfPairs(nums = [29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 16

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 17

Answer: assert Solution().countOfPairs(nums = [15, 10, 5, 10, 15, 10, 5, 10, 15]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 151

Answer: assert Solution().countOfPairs(nums = [100, 50, 100, 50, 100, 50, 100]) == 0

Answer: assert Solution().countOfPairs(nums = [500, 300, 200, 400, 500]) == 872408777

Answer: assert Solution().countOfPairs(nums = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980]) == 846458288

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

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

Answer: assert Solution().countOfPairs(nums = [2000, 1, 2000, 1, 2000, 1, 2000, 1, 2000, 1, 2000, 1, 2000, 1, 2000, 1, 2000, 1, 2000, 1]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950]) == 21

Answer: assert Solution().countOfPairs(nums = [1, 10, 100, 1000, 1, 10, 100, 1000, 1, 10, 100, 1000, 1, 10, 100, 1000, 1, 10, 100, 1000]) == 0

Answer: assert Solution().countOfPairs(nums = [500, 1000, 750, 250, 500, 1000]) == 0

Answer: assert Solution().countOfPairs(nums = [100, 50, 25, 12, 6, 3, 2, 1, 1, 1]) == 11

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 21

Answer: assert Solution().countOfPairs(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 53130

Answer: assert Solution().countOfPairs(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 0

Answer: assert Solution().countOfPairs(nums = [2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986, 1985, 1984, 1983, 1982, 1981]) == 882480825

Answer: assert Solution().countOfPairs(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 31

Answer: assert Solution().countOfPairs(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1771

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

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

Answer: assert Solution().countOfPairs(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 21

Answer: assert Solution().countOfPairs(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30]) == 657505568

Answer: assert Solution().countOfPairs(nums = [500, 500, 250, 750, 500, 500, 250, 750, 500, 500]) == 0

Answer: assert Solution().countOfPairs(nums = [100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200]) == 0

Answer: assert Solution().countOfPairs(nums = [3, 6, 9, 12, 15, 18, 21]) == 120

Answer: assert Solution().countOfPairs(nums = [500, 1, 500, 1, 500, 1, 500, 1, 500, 1, 500, 1, 500, 1, 500, 1, 500, 1, 500, 1]) == 0

Answer: assert Solution().countOfPairs(nums = [1, 100, 2, 99, 3, 98, 4, 97, 5, 96, 6, 95, 7, 94, 8, 93, 9, 92, 10, 91]) == 0

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

Answer: assert Solution().countOfPairs(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]) == 21

Answer: assert Solution().countOfPairs(nums = [10, 15, 10, 20, 15, 25, 20, 30, 25, 35, 30, 40, 35, 45, 40]) == 0

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

Answer: assert Solution().countOfPairs(nums = [1, 10, 100, 1000, 10, 1, 1, 10, 100, 1000, 10, 1, 1, 10, 100, 1000, 10, 1, 1, 10]) == 0

Answer: assert Solution().countOfPairs(nums = [1000, 500, 250, 125, 62, 31, 15, 7, 3, 1]) == 11

Answer: assert Solution().countOfPairs(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 428536

Answer: assert Solution().countOfPairs(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 184756

Answer: assert Solution().countOfPairs(nums = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == 11

Answer: assert Solution().countOfPairs(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4]) == 14

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

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 16

Answer: assert Solution().countOfPairs(nums = [71, 67, 61, 59, 53, 47, 43, 41, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2]) == 231

Answer: assert Solution().countOfPairs(nums = [500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519]) == 105350580

Answer: assert Solution().countOfPairs(nums = [1, 10, 100, 1000, 1000, 100, 10, 1, 10, 100, 1000, 1000, 100, 10, 1]) == 0

Answer: assert Solution().countOfPairs(nums = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985]) == 215996956

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

Answer: assert Solution().countOfPairs(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 21

Answer: assert Solution().countOfPairs(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]) == 231

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

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

Answer: assert Solution().countOfPairs(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 747379722

Answer: assert Solution().countOfPairs(nums = [500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500]) == 105350580

Answer: assert Solution().countOfPairs(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6]) == 19

Answer: assert Solution().countOfPairs(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 26

Answer: assert Solution().countOfPairs(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, 26, 25, 27, 26, 28, 27, 29, 28, 30, 29, 31, 30, 32, 31, 33, 32, 34, 33, 35, 34, 36, 35, 37, 36, 38, 37, 39, 38, 40, 39, 41, 40, 42, 41, 43, 42, 44, 43, 45, 44, 46, 45, 47, 46, 48, 47, 49, 48, 50, 49, 51, 50, 52, 51, 53, 52, 54, 53, 55, 54, 56, 55, 57, 56, 58, 57, 59, 58, 60, 59, 61, 60, 62, 61, 63, 62, 64, 63, 65, 64, 66, 65, 67, 66, 68, 67, 69, 68, 70, 69, 71, 70, 72, 71, 73, 72, 74, 73, 75, 74, 76, 75, 77, 76, 78, 77, 79, 78, 80, 79, 81, 80, 82, 81, 83, 82, 84, 83, 85, 84, 86, 85, 87, 86, 88, 87, 89, 88, 90, 89, 91, 90, 92, 91, 93, 92, 94, 93, 95, 94, 96, 95, 97, 96, 98, 97, 99, 98, 100]) == 0

Answer: assert Solution().countOfPairs(nums = [200, 150, 100, 50, 0, 50, 100, 150, 200]) == 1

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

Answer: assert Solution().countOfPairs(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 0

Answer: assert Solution().countOfPairs(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 231

Answer: assert Solution().countOfPairs(nums = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990]) == 528016600

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

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

Answer: assert Solution().countOfPairs(nums = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) == 659632782

Answer: assert Solution().countOfPairs(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 3268760

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

Answer: assert Solution().countOfPairs(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 888030

Answer: assert Solution().countOfPairs(nums = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991]) == 382248421

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
    def countOfPairs(self, nums: List[int]) -> int:
        mod = 10**9 + 7
        n, m = len(nums), max(nums)
        f = [[0] * (m + 1) for _ in range(n)]
        for j in range(nums[0] + 1):
            f[0][j] = 1
        for i in range(1, n):
            s = list(accumulate(f[i - 1]))
            for j in range(nums[i] + 1):
                k = min(j, j + nums[i - 1] - nums[i])
                if k >= 0:
                    f[i][j] = s[k] % mod
        return sum(f[-1][: nums[-1] + 1]) % mod