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

PROBLEM:
You are given a string s and an integer k. Your task is to find the maximum difference between the frequency of two characters, freq[a] - freq[b], in a substring subs of s, such that:

subs has a size of at least k.
Character a has an odd frequency in subs.
Character b has an even frequency in subs.

Return the maximum difference.
Note that subs can contain more than 2 distinct characters.

Example 1:

Input: s = "12233", k = 4
Output: -1
Explanation:
For the substring "12233", the frequency of '1' is 1 and the frequency of '3' is 2. The difference is 1 - 2 = -1.

Example 2:

Input: s = "1122211", k = 3
Output: 1
Explanation:
For the substring "11222", the frequency of '2' is 3 and the frequency of '1' is 2. The difference is 3 - 2 = 1.

Example 3:

Input: s = "110", k = 3
Output: -1

Constraints:

3 <= s.length <= 3 * 104
s consists only of digits '0' to '4'.
The input is generated that at least one substring has a character with an even frequency and a character with an odd frequency.
1 <= k <= s.length

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

SOLUTION:

Question:
PROBLEM:
You are given a string s and an integer k. Your task is to find the maximum difference between the frequency of two characters, freq[a] - freq[b], in a substring subs of s, such that:

subs has a size of at least k.
Character a has an odd frequency in subs.
Character b has an even frequency in subs.

Return the maximum difference.
Note that subs can contain more than 2 distinct characters.

Example 1:

Input: s = "12233", k = 4
Output: -1
Explanation:
For the substring "12233", the frequency of '1' is 1 and the frequency of '3' is 2. The difference is 1 - 2 = -1.

Example 2:

Input: s = "1122211", k = 3
Output: 1
Explanation:
For the substring "11222", the frequency of '2' is 3 and the frequency of '1' is 2. The difference is 3 - 2 = 1.

Example 3:

Input: s = "110", k = 3
Output: -1

Constraints:

3 <= s.length <= 3 * 104
s consists only of digits '0' to '4'.
The input is generated that at least one substring has a character with an even frequency and a character with an odd frequency.
1 <= k <= s.length

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

SOLUTION:

assert Solution().maxDifference(s = "2222222", k = 3) == -inf

assert Solution().maxDifference(s = "1010101010", k = 4) == 1

assert Solution().maxDifference(s = "000111", k = 2) == 1

assert Solution().maxDifference(s = "101010101", k = 4) == 1

assert Solution().maxDifference(s = "444333222111", k = 6) == 1

assert Solution().maxDifference(s = "4444444", k = 3) == -inf

assert Solution().maxDifference(s = "12340", k = 2) == -inf

assert Solution().maxDifference(s = "111222333", k = 6) == 1

assert Solution().maxDifference(s = "110", k = 3) == -1

assert Solution().maxDifference(s = "1122211", k = 3) == 1

assert Solution().maxDifference(s = "0123401234", k = 5) == -1

assert Solution().maxDifference(s = "000000000000", k = 5) == -inf

assert Solution().maxDifference(s = "111223344", k = 5) == 1

assert Solution().maxDifference(s = "44444444", k = 4) == -inf

assert Solution().maxDifference(s = "12233", k = 4) == -1

assert Solution().maxDifference(s = "444444444", k = 2) == -inf

assert Solution().maxDifference(s = "111111111111", k = 7) == -inf

assert Solution().maxDifference(s = "00000", k = 2) == -inf

assert Solution().maxDifference(s = "4444444", k = 5) == -inf

assert Solution().maxDifference(s = "2222222", k = 5) == -inf

assert Solution().maxDifference(s = "012340123", k = 3) == -1

assert Solution().maxDifference(s = "43210", k = 3) == -inf

assert Solution().maxDifference(s = "111222333", k = 5) == 1

assert Solution().maxDifference(s = "101010101010", k = 5) == 1

assert Solution().maxDifference(s = "000111000", k = 5) == 1

assert Solution().maxDifference(s = "432101234", k = 4) == -1

assert Solution().maxDifference(s = "3333333", k = 7) == -inf

assert Solution().maxDifference(s = "111222333444555", k = 9) == 1

assert Solution().maxDifference(s = "012340123401234", k = 8) == 1

assert Solution().maxDifference(s = "111222333444000", k = 7) == 1

assert Solution().maxDifference(s = "444000111222", k = 7) == 1

assert Solution().maxDifference(s = "11222333444", k = 7) == 1

assert Solution().maxDifference(s = "12343211234321", k = 5) == 1

assert Solution().maxDifference(s = "012340123401234", k = 5) == 1

assert Solution().maxDifference(s = "432104321043210", k = 5) == 1

assert Solution().maxDifference(s = "000000000000", k = 7) == -inf

assert Solution().maxDifference(s = "121212121212121", k = 9) == 1

assert Solution().maxDifference(s = "1001001001001", k = 9) == 3

assert Solution().maxDifference(s = "000000000000000", k = 10) == -inf

assert Solution().maxDifference(s = "0011223344", k = 6) == -1

assert Solution().maxDifference(s = "111222333444", k = 9) == 1

assert Solution().maxDifference(s = "123401234012340", k = 8) == 1

assert Solution().maxDifference(s = "000111222333444", k = 8) == 1

assert Solution().maxDifference(s = "111111111111111", k = 6) == -inf

assert Solution().maxDifference(s = "123212321232123", k = 7) == 3

assert Solution().maxDifference(s = "123451234512345", k = 9) == 1

assert Solution().maxDifference(s = "1223333321", k = 7) == 3

assert Solution().maxDifference(s = "123412341234", k = 6) == 1

assert Solution().maxDifference(s = "0011223344", k = 7) == -1

assert Solution().maxDifference(s = "422411422411", k = 6) == 1

assert Solution().maxDifference(s = "432104321043210", k = 7) == 1

assert Solution().maxDifference(s = "432104321043210", k = 8) == 1

assert Solution().maxDifference(s = "101010101010101", k = 8) == 1

assert Solution().maxDifference(s = "123423143214321", k = 5) == 1

assert Solution().maxDifference(s = "1234012340", k = 5) == -1

assert Solution().maxDifference(s = "123451234512345", k = 15) == -inf

assert Solution().maxDifference(s = "2222222111111", k = 7) == 5

assert Solution().maxDifference(s = "000111222333444", k = 9) == 1

assert Solution().maxDifference(s = "012340123401234", k = 7) == 1

assert Solution().maxDifference(s = "012012012012", k = 5) == 1

assert Solution().maxDifference(s = "122331223312233", k = 5) == 3

assert Solution().maxDifference(s = "000111222333444", k = 7) == 1

assert Solution().maxDifference(s = "333333333333", k = 10) == -inf

assert Solution().maxDifference(s = "432101234321012", k = 6) == 1

assert Solution().maxDifference(s = "123123123123", k = 6) == 1

assert Solution().maxDifference(s = "122112211221122", k = 5) == 1

assert Solution().maxDifference(s = "420240240240240", k = 8) == 1

assert Solution().maxDifference(s = "122221111222211", k = 9) == 3

Answer: assert Solution().maxDifference(s = "2222222", k = 3) == -inf

Answer: assert Solution().maxDifference(s = "1010101010", k = 4) == 1

Answer: assert Solution().maxDifference(s = "000111", k = 2) == 1

Answer: assert Solution().maxDifference(s = "101010101", k = 4) == 1

Answer: assert Solution().maxDifference(s = "444333222111", k = 6) == 1

Answer: assert Solution().maxDifference(s = "4444444", k = 3) == -inf

Answer: assert Solution().maxDifference(s = "12340", k = 2) == -inf

Answer: assert Solution().maxDifference(s = "111222333", k = 6) == 1

Answer: assert Solution().maxDifference(s = "110", k = 3) == -1

Answer: assert Solution().maxDifference(s = "1122211", k = 3) == 1

Answer: assert Solution().maxDifference(s = "0123401234", k = 5) == -1

Answer: assert Solution().maxDifference(s = "000000000000", k = 5) == -inf

Answer: assert Solution().maxDifference(s = "111223344", k = 5) == 1

Answer: assert Solution().maxDifference(s = "44444444", k = 4) == -inf

Answer: assert Solution().maxDifference(s = "12233", k = 4) == -1

Answer: assert Solution().maxDifference(s = "444444444", k = 2) == -inf

Answer: assert Solution().maxDifference(s = "111111111111", k = 7) == -inf

Answer: assert Solution().maxDifference(s = "00000", k = 2) == -inf

Answer: assert Solution().maxDifference(s = "4444444", k = 5) == -inf

Answer: assert Solution().maxDifference(s = "2222222", k = 5) == -inf

Answer: assert Solution().maxDifference(s = "012340123", k = 3) == -1

Answer: assert Solution().maxDifference(s = "43210", k = 3) == -inf

Answer: assert Solution().maxDifference(s = "111222333", k = 5) == 1

Answer: assert Solution().maxDifference(s = "101010101010", k = 5) == 1

Answer: assert Solution().maxDifference(s = "000111000", k = 5) == 1

Answer: assert Solution().maxDifference(s = "432101234", k = 4) == -1

Answer: assert Solution().maxDifference(s = "33333322222111111", k = 7) == 3

Answer: assert Solution().maxDifference(s = "3333333", k = 7) == -inf

Answer: assert Solution().maxDifference(s = "44444444444444444444444444444444444444444444", k = 25) == -inf

Answer: assert Solution().maxDifference(s = "101010101010101010101010101010101010101010101010", k = 20) == 1

Answer: assert Solution().maxDifference(s = "012340123401234", k = 11) == 1

Answer: assert Solution().maxDifference(s = "111222333444555", k = 9) == 1

Answer: assert Solution().maxDifference(s = "012340123401234", k = 8) == 1

Answer: assert Solution().maxDifference(s = "44332211004433221100", k = 12) == 1

Answer: assert Solution().maxDifference(s = "111222333444000", k = 7) == 1

Answer: assert Solution().maxDifference(s = "222222111111000000333333", k = 12) == 3

Answer: assert Solution().maxDifference(s = "444000111222", k = 7) == 1

Answer: assert Solution().maxDifference(s = "0000000000000000000000000000", k = 15) == -inf

Answer: assert Solution().maxDifference(s = "11222333444", k = 7) == 1

Answer: assert Solution().maxDifference(s = "12343211234321", k = 5) == 1

Answer: assert Solution().maxDifference(s = "012340123401234", k = 5) == 1

Answer: assert Solution().maxDifference(s = "432104321043210", k = 5) == 1

Answer: assert Solution().maxDifference(s = "000111222333444000111222333444", k = 15) == 1

Answer: assert Solution().maxDifference(s = "11111111111111111111111111111111111111111111", k = 15) == -inf

Answer: assert Solution().maxDifference(s = "4333222211110000", k = 7) == 1

Answer: assert Solution().maxDifference(s = "000000000000", k = 7) == -inf

Answer: assert Solution().maxDifference(s = "2222111122221111", k = 8) == 3

Answer: assert Solution().maxDifference(s = "5432101234543210123", k = 13) == 1

Answer: assert Solution().maxDifference(s = "32104321043210432104321043210", k = 11) == 1

Answer: assert Solution().maxDifference(s = "121212121212121", k = 9) == 1

Answer: assert Solution().maxDifference(s = "4040404040404040", k = 9) == 1

Answer: assert Solution().maxDifference(s = "11223344555544332211", k = 9) == 1

Answer: assert Solution().maxDifference(s = "4321043210432104321043210", k = 7) == 1

Answer: assert Solution().maxDifference(s = "3333333333333333333333333333333333333333333333333", k = 25) == -inf

Answer: assert Solution().maxDifference(s = "1010101010101010101010101010", k = 10) == 1

Answer: assert Solution().maxDifference(s = "333322221111000044443333222211110000", k = 16) == 3

Answer: assert Solution().maxDifference(s = "010101010101010101", k = 5) == 1

Answer: assert Solution().maxDifference(s = "00001111222233334444", k = 10) == 1

Answer: assert Solution().maxDifference(s = "44444444444444444444", k = 20) == -inf

Answer: assert Solution().maxDifference(s = "1001001001001", k = 9) == 3

Answer: assert Solution().maxDifference(s = "000000000000000", k = 10) == -inf

Answer: assert Solution().maxDifference(s = "123123123123123123123", k = 12) == 1

Answer: assert Solution().maxDifference(s = "44444444444444444444444444", k = 20) == -inf

Answer: assert Solution().maxDifference(s = "123412341234123412341234", k = 12) == 1

Answer: assert Solution().maxDifference(s = "5555544444333332222211111", k = 15) == 3

Answer: assert Solution().maxDifference(s = "0011223344", k = 6) == -1

Answer: assert Solution().maxDifference(s = "111222333444", k = 9) == 1

Answer: assert Solution().maxDifference(s = "123401234012340", k = 8) == 1

Answer: assert Solution().maxDifference(s = "000111222333444", k = 8) == 1

Answer: assert Solution().maxDifference(s = "12221111222211112222", k = 10) == 3

Answer: assert Solution().maxDifference(s = "111111111111111", k = 6) == -inf

Answer: assert Solution().maxDifference(s = "123212321232123", k = 7) == 3

Answer: assert Solution().maxDifference(s = "01234012340123401234", k = 10) == 1

Answer: assert Solution().maxDifference(s = "314213421342134213", k = 6) == 1

Answer: assert Solution().maxDifference(s = "404040404040404040", k = 15) == 1

Answer: assert Solution().maxDifference(s = "123451234512345", k = 9) == 1

Answer: assert Solution().maxDifference(s = "1223333321", k = 7) == 3

Answer: assert Solution().maxDifference(s = "12321232123212321", k = 10) == 3

Answer: assert Solution().maxDifference(s = "123412341234", k = 6) == 1

Answer: assert Solution().maxDifference(s = "444333222111000444333222111000444", k = 12) == 3

Answer: assert Solution().maxDifference(s = "0011223344", k = 7) == -1

Answer: assert Solution().maxDifference(s = "12233322333223332233322333", k = 12) == 7

Answer: assert Solution().maxDifference(s = "0000000011111111222222223333333344444444", k = 18) == 5

Answer: assert Solution().maxDifference(s = "00112233445566778899", k = 15) == -1

Answer: assert Solution().maxDifference(s = "44443333222211110000", k = 12) == 1

Answer: assert Solution().maxDifference(s = "422411422411", k = 6) == 1

Answer: assert Solution().maxDifference(s = "1221221221221221221221221221221", k = 13) == 9

Answer: assert Solution().maxDifference(s = "432104321043210", k = 7) == 1

Answer: assert Solution().maxDifference(s = "222111000333222111000333222111000", k = 15) == 3

Answer: assert Solution().maxDifference(s = "1111100000222223333344444", k = 15) == 3

Answer: assert Solution().maxDifference(s = "11223344001122334400", k = 10) == 1

Answer: assert Solution().maxDifference(s = "333444333444333444333444333444333444", k = 18) == 3

Answer: assert Solution().maxDifference(s = "432104321043210", k = 8) == 1

Answer: assert Solution().maxDifference(s = "012340123401234", k = 10) == 1

Answer: assert Solution().maxDifference(s = "2222111100004444", k = 10) == 1

Answer: assert Solution().maxDifference(s = "101010101010101", k = 8) == 1

Answer: assert Solution().maxDifference(s = "4321043210432104321043210", k = 11) == 1

Answer: assert Solution().maxDifference(s = "123423143214321", k = 5) == 1

Answer: assert Solution().maxDifference(s = "122122122122122122122122122122122122122122122122", k = 10) == 15

Answer: assert Solution().maxDifference(s = "444444333333222222111111000000", k = 15) == 3

Answer: assert Solution().maxDifference(s = "11111111111111111111", k = 15) == -inf

Answer: assert Solution().maxDifference(s = "1112222233333334444444444", k = 15) == 7

Answer: assert Solution().maxDifference(s = "121212121212121212121212121", k = 13) == 1

Answer: assert Solution().maxDifference(s = "001122001122001122", k = 10) == 1

Answer: assert Solution().maxDifference(s = "12341234123412341234", k = 14) == 1

Answer: assert Solution().maxDifference(s = "123123123123123123", k = 8) == 1

Answer: assert Solution().maxDifference(s = "44332211000044332211", k = 12) == 1

Answer: assert Solution().maxDifference(s = "11111222223333344444", k = 10) == 3

Answer: assert Solution().maxDifference(s = "1234012340", k = 5) == -1

Answer: assert Solution().maxDifference(s = "123451234512345", k = 15) == -inf

Answer: assert Solution().maxDifference(s = "1111111111111111111111111111", k = 15) == -inf

Answer: assert Solution().maxDifference(s = "0000111100001111", k = 8) == 3

Answer: assert Solution().maxDifference(s = "2222222111111", k = 7) == 5

Answer: assert Solution().maxDifference(s = "11112222333344440000", k = 10) == 1

Answer: assert Solution().maxDifference(s = "000111222333444", k = 9) == 1

Answer: assert Solution().maxDifference(s = "000111222333444000111", k = 15) == 1

Answer: assert Solution().maxDifference(s = "00110011001100110011001100110011", k = 14) == 1

Answer: assert Solution().maxDifference(s = "012340123401234", k = 7) == 1

Answer: assert Solution().maxDifference(s = "012012012012", k = 5) == 1

Answer: assert Solution().maxDifference(s = "10101010101010101010101010101010", k = 15) == 1

Answer: assert Solution().maxDifference(s = "122331223312233", k = 5) == 3

Answer: assert Solution().maxDifference(s = "333332222221111111", k = 12) == 5

Answer: assert Solution().maxDifference(s = "1122334455112233", k = 12) == 1

Answer: assert Solution().maxDifference(s = "3333222211110000", k = 8) == 1

Answer: assert Solution().maxDifference(s = "000111222333444", k = 7) == 1

Answer: assert Solution().maxDifference(s = "333333333333", k = 10) == -inf

Answer: assert Solution().maxDifference(s = "432101234321012", k = 6) == 1

Answer: assert Solution().maxDifference(s = "123123123123", k = 6) == 1

Answer: assert Solution().maxDifference(s = "012340123401234012340123401234012340123401234", k = 20) == 1

Answer: assert Solution().maxDifference(s = "222222222111111111000000000", k = 12) == 7

Answer: assert Solution().maxDifference(s = "122112211221122", k = 5) == 1

Answer: assert Solution().maxDifference(s = "01010101010101010101010", k = 20) == 1

Answer: assert Solution().maxDifference(s = "420240240240240", k = 8) == 1

Answer: assert Solution().maxDifference(s = "1234023412340234", k = 7) == 1

Answer: assert Solution().maxDifference(s = "122221111222211", k = 9) == 3

Answer: assert Solution().maxDifference(s = "1112222211133344444444", k = 18) == 3

Answer: assert Solution().maxDifference(s = "211221122112211221122112211", k = 13) == 1

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
  def maxDifference(self, s: str, k: int) -> int:
    ans = -math.inf
    permutations = [(a, b) for a in '01234' for b in '01234' if a != b]

    for a, b in permutations:
      # minDiff[(parityA, parityB)] := min(a - b) of all valid windows with
      # parityA and parityB
      minDiff = collections.defaultdict(lambda: math.inf)
      prefixA = [0]  # prefixA[i] := the number of 'a's in s[0..i)
      prefixB = [0]  # prefixB[i] := the number of 'b's in s[0..i)

      l = 0
      for r, c in enumerate(s):
        prefixA.append(prefixA[-1] + int(c == a))
        prefixB.append(prefixB[-1] + int(c == b))
        while (r - l + 1 >= k and  # the window size >= k
               prefixA[l] < prefixA[-1] and  # the number of 'a's > 0
               prefixB[l] < prefixB[-1]):  # the number of 'b's > 0
          paritiesKey = (prefixA[l] % 2, prefixB[l] % 2)
          minDiff[paritiesKey] = min(minDiff[paritiesKey],
                                     prefixA[l] - prefixB[l])
          l += 1
        ans = max(ans, (prefixA[-1] - prefixB[-1]) -
                  minDiff[(1 - prefixA[-1] % 2, prefixB[-1] % 2)])

    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 n x n square matrix of integers grid. Return the matrix such that:

The diagonals in the bottom-left triangle (including the middle diagonal) are sorted in non-increasing order.
The diagonals in the top-right triangle are sorted in non-decreasing order.

Example 1:

Input: grid = [[1,7,3],[9,8,2],[4,5,6]]
Output: [[8,2,3],[9,6,7],[4,5,1]]
Explanation:

The diagonals with a black arrow (bottom-left triangle) should be sorted in non-increasing order:

[1, 8, 6] becomes [8, 6, 1].
[9, 5] and [4] remain unchanged.

The diagonals with a blue arrow (top-right triangle) should be sorted in non-decreasing order:

[7, 2] becomes [2, 7].
[3] remains unchanged.

Example 2:

Input: grid = [[0,1],[1,2]]
Output: [[2,1],[1,0]]
Explanation:

The diagonals with a black arrow must be non-increasing, so [0, 2] is changed to [2, 0]. The other diagonals are already in the correct order.

Example 3:

Input: grid = [[1]]
Output: [[1]]
Explanation:
Diagonals with exactly one element are already in order, so no changes are needed.

Constraints:

grid.length == grid[i].length == n
1 <= n <= 10
-105 <= grid[i][j] <= 105

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

SOLUTION:

Question:
PROBLEM:
You are given an n x n square matrix of integers grid. Return the matrix such that:

The diagonals in the bottom-left triangle (including the middle diagonal) are sorted in non-increasing order.
The diagonals in the top-right triangle are sorted in non-decreasing order.

Example 1:

Input: grid = [[1,7,3],[9,8,2],[4,5,6]]
Output: [[8,2,3],[9,6,7],[4,5,1]]
Explanation:

The diagonals with a black arrow (bottom-left triangle) should be sorted in non-increasing order:

[1, 8, 6] becomes [8, 6, 1].
[9, 5] and [4] remain unchanged.

The diagonals with a blue arrow (top-right triangle) should be sorted in non-decreasing order:

[7, 2] becomes [2, 7].
[3] remains unchanged.

Example 2:

Input: grid = [[0,1],[1,2]]
Output: [[2,1],[1,0]]
Explanation:

The diagonals with a black arrow must be non-increasing, so [0, 2] is changed to [2, 0]. The other diagonals are already in the correct order.

Example 3:

Input: grid = [[1]]
Output: [[1]]
Explanation:
Diagonals with exactly one element are already in order, so no changes are needed.

Constraints:

grid.length == grid[i].length == n
1 <= n <= 10
-105 <= grid[i][j] <= 105

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

SOLUTION:

assert Solution().sortMatrix(grid = [[1]]) == [[1]]

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

Answer: assert Solution().sortMatrix(grid = [[0,1],[1,2]]) == [[2, 1], [1, 0]]

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

Answer: assert Solution().sortMatrix(grid = [[-10,-20,-30],[-40,-50,-60],[-70,-80,-90]]) == [[-10, -60, -30], [-40, -50, -20], [-70, -80, -90]]

Answer: assert Solution().sortMatrix(grid = [[10,-5,3],[2,8,0],[-3,4,6]]) == [[10, -5, 3], [4, 8, 0], [-3, 2, 6]]

Answer: assert Solution().sortMatrix(grid = [[1]]) == [[1]]

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

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

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

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

Answer: assert Solution().sortMatrix(grid = [[-1,-2,-3],[-4,-5,-6],[-7,-8,-9]]) == [[-1, -6, -3], [-4, -5, -2], [-7, -8, -9]]

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

Answer: assert Solution().sortMatrix(grid = [[-5,3,0],[-1,2,4],[1,-4,-3]]) == [[2, 3, 0], [-1, -3, 4], [1, -4, -5]]

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

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

Answer: assert Solution().sortMatrix(grid = [[100, -100, 50, -50], [-50, 50, -100, 100], [25, -25, 75, -75], [-75, 75, -25, 25]]) == [[100, -100, 50, -50], [-25, 75, -100, 100], [75, -25, 50, -75], [-75, 25, -50, 25]]

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

Answer: assert Solution().sortMatrix(grid = [[-1,0,1],[-2,0,2],[-3,0,3]]) == [[3, 0, 1], [0, 0, 2], [-3, -2, -1]]

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

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

Answer: assert Solution().sortMatrix(grid = [[-10, 0, 10, 20], [30, -20, 15, -5], [-30, -15, 25, 10], [5, 5, 0, -10]]) == [[25, 0, -5, 20], [30, -10, 10, 10], [5, 0, -10, 15], [5, -30, -15, -20]]

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

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

Answer: assert Solution().sortMatrix(grid = [[100, 99, 98, 97, 96], [95, 94, 93, 92, 91], [90, 89, 88, 87, 86], [85, 84, 83, 82, 81], [80, 79, 78, 77, 76]]) == [[100, 81, 86, 91, 96], [95, 94, 87, 92, 97], [90, 89, 88, 93, 98], [85, 84, 83, 82, 99], [80, 79, 78, 77, 76]]

Answer: assert Solution().sortMatrix(grid = [[-5,10,-15,20],[-25,30,-35,40],[-45,50,-55,60],[-65,70,-75,80]]) == [[80, -35, -15, 20], [50, 30, 10, 40], [70, -25, -5, 60], [-65, -45, -75, -55]]

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

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

Answer: assert Solution().sortMatrix(grid = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == [[1, 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().sortMatrix(grid = [[-100000,100000,0],[0,0,0],[-100000,100000,0]]) == [[0, 0, 0], [100000, 0, 100000], [-100000, 0, -100000]]

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

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

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

Answer: assert Solution().sortMatrix(grid = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) == [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]

Answer: assert Solution().sortMatrix(grid = [[30,25,20,15,10],[25,20,15,10,5],[20,15,10,5,0],[15,10,5,0,-5],[10,5,0,-5,-10]]) == [[30, -5, 0, 5, 10], [25, 20, 5, 10, 15], [20, 15, 10, 15, 20], [15, 10, 5, 0, 25], [10, 5, 0, -5, -10]]

Answer: assert Solution().sortMatrix(grid = [[-100, 100, -50, 50], [25, -25, 75, -75], [-150, 150, -200, 200], [5, -5, 10, -10]]) == [[-10, 75, -75, 50], [150, -25, 100, -50], [-5, 25, -100, 200], [5, -150, 10, -200]]

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

Answer: assert Solution().sortMatrix(grid = [[10,20,30,40],[50,60,70,80],[90,100,110,120],[130,140,150,160]]) == [[160, 20, 30, 40], [150, 110, 70, 80], [140, 100, 60, 120], [130, 90, 50, 10]]

Answer: assert Solution().sortMatrix(grid = [[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]) == [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]

Answer: assert Solution().sortMatrix(grid = [[-1,2,-3,4],[5,-6,7,-8],[9,0,-11,12],[13,-14,15,-16]]) == [[-1, 2, -8, 4], [15, -6, 7, -3], [9, 5, -11, 12], [13, -14, 0, -16]]

Answer: assert Solution().sortMatrix(grid = [[-100000, 100000, -50000, 50000], [100000, -100000, 50000, -50000], [-50000, 50000, -100000, 100000], [50000, -50000, 100000, -100000]]) == [[-100000, 50000, -50000, 50000], [100000, -100000, 100000, -50000], [-50000, 100000, -100000, 100000], [50000, -50000, 50000, -100000]]

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

Answer: assert Solution().sortMatrix(grid = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [2, 3, 4, 5, 6], [6, 5, 4, 3, 2], [3, 4, 5, 6, 7]]) == [[7, 2, 2, 1, 5], [6, 4, 2, 3, 4], [5, 5, 4, 3, 6], [6, 5, 4, 3, 5], [3, 4, 2, 3, 1]]

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

Answer: assert Solution().sortMatrix(grid = [[1000,-1000,500],[200,300,-200],[1500,50,250]]) == [[1000, -1000, 500], [200, 300, -200], [1500, 50, 250]]

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

Answer: assert Solution().sortMatrix(grid = [[0,10,20,30],[10,20,30,40],[20,30,40,50],[30,40,50,60]]) == [[60, 10, 20, 30], [50, 40, 30, 40], [40, 30, 20, 50], [30, 20, 10, 0]]

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

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

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

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

Answer: assert Solution().sortMatrix(grid = [[5,10,15,20,25],[30,35,40,45,50],[60,65,70,75,80],[85,90,95,100,105],[110,115,120,125,130]]) == [[130, 10, 15, 20, 25], [125, 100, 40, 45, 50], [120, 95, 70, 75, 80], [115, 90, 65, 35, 105], [110, 85, 60, 30, 5]]

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

Answer: assert Solution().sortMatrix(grid = [[100, 50, 10], [200, 150, 60], [300, 250, 120]]) == [[150, 50, 10], [250, 120, 60], [300, 200, 100]]

Answer: assert Solution().sortMatrix(grid = [[10, -20, 30, 40], [-10, 5, 6, 15], [25, 1, -15, 20], [5, 35, 2, 4]]) == [[10, -20, 15, 40], [2, 5, 6, 30], [35, 1, 4, 20], [5, 25, -10, -15]]

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

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

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

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

Answer: assert Solution().sortMatrix(grid = [[100000,-100000,50000,-50000],[25000,75000,-25000,25000],[-50000,50000,100000,-100000],[25000,-25000,25000,75000]]) == [[100000, -100000, 25000, -50000], [50000, 100000, -100000, 50000], [-25000, 25000, 75000, -25000], [25000, -50000, 25000, 75000]]

Answer: assert Solution().sortMatrix(grid = [[-1,-2,-3,-4],[-2,-3,-4,-5],[-3,-4,-5,-6],[-4,-5,-6,-7]]) == [[-1, -6, -5, -4], [-2, -3, -4, -3], [-3, -4, -5, -2], [-4, -5, -6, -7]]

Answer: assert Solution().sortMatrix(grid = [[10, -5, 7, 3], [15, 20, -1, 8], [5, 12, 18, 4], [9, 1, 6, 11]]) == [[20, -5, 7, 3], [15, 18, -1, 8], [5, 12, 11, 4], [9, 1, 6, 10]]

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

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

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

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

Answer: assert Solution().sortMatrix(grid = [[-5, -1, 0, 2], [4, 3, 1, -2], [2, 0, -3, -1], [3, 2, 1, -5]]) == [[3, -1, -2, 2], [4, -3, -1, 0], [2, 1, -5, 1], [3, 2, 0, -5]]

Answer: assert Solution().sortMatrix(grid = [[100,90,80,70,60],[50,40,30,20,10],[0,-10,-20,-30,-40],[-50,-60,-70,-80,-90],[-100,-110,-120,-130,-140]]) == [[100, -90, -40, 10, 60], [50, 40, -30, 20, 70], [0, -10, -20, 30, 80], [-50, -60, -70, -80, 90], [-100, -110, -120, -130, -140]]

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

Answer: assert Solution().sortMatrix(grid = [[5, 10, 15, 20], [14, 9, 4, -1], [13, 8, 3, 2], [12, 7, 2, 1]]) == [[9, 2, -1, 20], [14, 5, 4, 15], [13, 8, 3, 10], [12, 7, 2, 1]]

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

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

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

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

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

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

Answer: assert Solution().sortMatrix(grid = [[20, 10, 5, 1], [15, 25, 12, 6], [8, 9, 14, 11], [4, 7, 13, 3]]) == [[25, 10, 5, 1], [15, 20, 11, 6], [8, 13, 14, 12], [4, 7, 9, 3]]

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

Answer: assert Solution().sortMatrix(grid = [[-10,-20,-30],[-20,-30,-40],[-30,-40,-50]]) == [[-10, -40, -30], [-20, -30, -20], [-30, -40, -50]]

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 sortMatrix(self, grid: List[List[int]]) -> List[List[int]]:
        n = len(grid)
        for k in range(n - 2, -1, -1):
            i, j = k, 0
            t = []
            while i < n and j < n:
                t.append(grid[i][j])
                i += 1
                j += 1
            t.sort()
            i, j = k, 0
            while i < n and j < n:
                grid[i][j] = t.pop()
                i += 1
                j += 1
        for k in range(n - 2, 0, -1):
            i, j = k, n - 1
            t = []
            while i >= 0 and j >= 0:
                t.append(grid[i][j])
                i -= 1
                j -= 1
            t.sort()
            i, j = k, n - 1
            while i >= 0 and j >= 0:
                grid[i][j] = t.pop()
                i -= 1
                j -= 1
        return grid


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

PROBLEM:
You are given an integer array groups, where groups[i] represents the size of the ith group. You are also given an integer array elements.
Your task is to assign one element to each group based on the following rules:

An element at index j can be assigned to a group i if groups[i] is divisible by elements[j].
If there are multiple elements that can be assigned, assign the element with the smallest index j.
If no element satisfies the condition for a group, assign -1 to that group.

Return an integer array assigned, where assigned[i] is the index of the element chosen for group i, or -1 if no suitable element exists.
Note: An element may be assigned to more than one group.

Example 1:

Input: groups = [8,4,3,2,4], elements = [4,2]
Output: [0,0,-1,1,0]
Explanation:

elements[0] = 4 is assigned to groups 0, 1, and 4.
elements[1] = 2 is assigned to group 3.
Group 2 cannot be assigned any element.

Example 2:

Input: groups = [2,3,5,7], elements = [5,3,3]
Output: [-1,1,0,-1]
Explanation:

elements[1] = 3 is assigned to group 1.
elements[0] = 5 is assigned to group 2.
Groups 0 and 3 cannot be assigned any element.

Example 3:

Input: groups = [10,21,30,41], elements = [2,1]
Output: [0,1,0,1]
Explanation:
elements[0] = 2 is assigned to the groups with even values, and elements[1] = 1 is assigned to the groups with odd values.

Constraints:

1 <= groups.length <= 105
1 <= elements.length <= 105
1 <= groups[i] <= 105
1 <= elements[i] <= 105

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

SOLUTION:

Question:
PROBLEM:
You are given an integer array groups, where groups[i] represents the size of the ith group. You are also given an integer array elements.
Your task is to assign one element to each group based on the following rules:

An element at index j can be assigned to a group i if groups[i] is divisible by elements[j].
If there are multiple elements that can be assigned, assign the element with the smallest index j.
If no element satisfies the condition for a group, assign -1 to that group.

Return an integer array assigned, where assigned[i] is the index of the element chosen for group i, or -1 if no suitable element exists.
Note: An element may be assigned to more than one group.

Example 1:

Input: groups = [8,4,3,2,4], elements = [4,2]
Output: [0,0,-1,1,0]
Explanation:

elements[0] = 4 is assigned to groups 0, 1, and 4.
elements[1] = 2 is assigned to group 3.
Group 2 cannot be assigned any element.

Example 2:

Input: groups = [2,3,5,7], elements = [5,3,3]
Output: [-1,1,0,-1]
Explanation:

elements[1] = 3 is assigned to group 1.
elements[0] = 5 is assigned to group 2.
Groups 0 and 3 cannot be assigned any element.

Example 3:

Input: groups = [10,21,30,41], elements = [2,1]
Output: [0,1,0,1]
Explanation:
elements[0] = 2 is assigned to the groups with even values, and elements[1] = 1 is assigned to the groups with odd values.

Constraints:

1 <= groups.length <= 105
1 <= elements.length <= 105
1 <= groups[i] <= 105
1 <= elements[i] <= 105

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

SOLUTION:

assert Solution().assignElements(groups = [1,1,1,1,1], elements = [1]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [10,10,10,10], elements = [5,10]) == [0, 0, 0, 0]

assert Solution().assignElements(groups = [8,4,3,2,4], elements = [4,2]) == [0, 0, -1, 1, 0]

assert Solution().assignElements(groups = [2,3,5,7], elements = [5,3,3]) == [-1, 1, 0, -1]

assert Solution().assignElements(groups = [3,6,9,12], elements = [3,6,9,12]) == [0, 0, 0, 0]

assert Solution().assignElements(groups = [10,5,15], elements = [5,10,15]) == [0, 0, 0]

assert Solution().assignElements(groups = [2,4,6,8], elements = [1,2,3,4]) == [0, 0, 0, 0]

assert Solution().assignElements(groups = [1,1,1,1], elements = [1]) == [0, 0, 0, 0]

assert Solution().assignElements(groups = [100,200,300], elements = [50,100,200]) == [0, 0, 0]

assert Solution().assignElements(groups = [10,21,30,41], elements = [2,1]) == [0, 1, 0, 1]

assert Solution().assignElements(groups = [5,10,15,20,25], elements = [5]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [5,5,5,5,5], elements = [5]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [15,20,25,30], elements = [5,10,15]) == [0, 0, 0, 0]

assert Solution().assignElements(groups = [10,10,10,10,10], elements = [5,2]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [5,10,15,20], elements = [5,10,20]) == [0, 0, 0, 0]

assert Solution().assignElements(groups = [5,10,15,20,25], elements = [5,10]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [7,14,21,28,35], elements = [7,14]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [7,14,28], elements = [7,14,28]) == [0, 0, 0]

assert Solution().assignElements(groups = [3,6,9,12,15], elements = [3,6]) == [0, 0, 0, 0, 0]

assert Solution().assignElements(groups = [100,200,300], elements = [10,20,30]) == [0, 0, 0]

Answer: assert Solution().assignElements(groups = [1,1,1,1,1], elements = [1]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10,10,10,10], elements = [5,10]) == [0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [11,22,33,44,55], elements = [11,22]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [8,4,3,2,4], elements = [4,2]) == [0, 0, -1, 1, 0]

Answer: assert Solution().assignElements(groups = [2,3,5,7], elements = [5,3,3]) == [-1, 1, 0, -1]

Answer: assert Solution().assignElements(groups = [3,3,3,3,3,3,3,3,3,3], elements = [1,3]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [1,2,3,4,5,6], elements = [1,2,3]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7,11,13,17], elements = [7,11,13,17]) == [0, 1, 2, 3]

Answer: assert Solution().assignElements(groups = [3,6,9,12], elements = [3,6,9,12]) == [0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12,15,20,25,30], elements = [3,4,5,6,10]) == [0, 0, 1, 2, 0]

Answer: assert Solution().assignElements(groups = [10,5,15], elements = [5,10,15]) == [0, 0, 0]

Answer: assert Solution().assignElements(groups = [100,200,300,400,500], elements = [10,20,30,40,50]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [2,4,6,8], elements = [1,2,3,4]) == [0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [1,1,1,1], elements = [1]) == [0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100,200,300,400,500], elements = [10,20,50]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [11,13,17,19,23,29,31,37,41,43], elements = [11,13,17,19,23,29,31,37,41,43]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Answer: assert Solution().assignElements(groups = [100,200,300], elements = [50,100,200]) == [0, 0, 0]

Answer: assert Solution().assignElements(groups = [1000,2000,3000,4000,5000], elements = [100,200,500]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10,21,30,41], elements = [2,1]) == [0, 1, 0, 1]

Answer: assert Solution().assignElements(groups = [5,10,15,20,25], elements = [5]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5,5,5,5,5], elements = [5]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [15,20,25,30], elements = [5,10,15]) == [0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100,200,300,400,500], elements = [100,50,25]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10,10,10,10,10], elements = [5,2]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12,24,36,48,60], elements = [12,6,3]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [1,2,3,4,5], elements = [1,2,3,4,5]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [2,4,6,8,10], elements = [1,2,3,4,5]) == [0, 0, 0, 0, 0]

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

Answer: assert Solution().assignElements(groups = [5,10,15,20], elements = [5,10,20]) == [0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5,10,15,20,25], elements = [5,10]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [6,6,6,6,6,6], elements = [2,3,6]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7,14,21,28,35], elements = [7,14]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7,14,28], elements = [7,14,28]) == [0, 0, 0]

Answer: assert Solution().assignElements(groups = [3,6,9,12,15], elements = [3,6]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100,200,300], elements = [10,20,30]) == [0, 0, 0]

Answer: assert Solution().assignElements(groups = [1024, 2048, 4096, 8192, 16384], elements = [2, 4, 8, 16, 32, 64]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000], elements = [100, 200, 500, 1000]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [123, 456, 789, 1011, 1213], elements = [1, 3, 9, 27, 81]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [500, 750, 1000, 1250, 1500, 1750, 2000], elements = [25, 50, 75, 100]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [23, 29, 31, 37, 41], elements = [1, 2, 3, 5, 7]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100, 200, 300, 400, 500, 600, 700], elements = [10, 20, 30, 40, 50]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [3, 6, 9, 12, 15, 18, 21, 24], elements = [3, 6, 9]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7,14,21,28,35], elements = [7,14,28,35]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100, 200, 300, 400, 500, 600, 700], elements = [10, 20, 50, 100]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 18, 24, 30, 36, 42], elements = [2, 3, 4, 6, 12]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [101, 103, 107, 109, 113, 127, 131, 137, 139, 149], elements = [1, 101, 103]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [21, 28, 35, 42, 49, 56], elements = [7, 14, 21, 28]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [11, 13, 17, 19, 23, 29, 31, 37, 41, 43], elements = [1, 2, 3, 4, 5]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [500, 1000, 1500, 2000, 2500, 3000], elements = [100, 200, 300, 400, 500]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [9, 18, 27, 36, 45, 54, 63, 72], elements = [9, 18, 27]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [11, 13, 17, 19, 23, 29], elements = [1, 11, 13, 17, 19, 23, 29]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10000, 20000, 30000, 40000, 50000], elements = [1000, 2000, 5000, 10000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [60, 120, 180, 240, 300, 360], elements = [6, 12, 18, 24, 30, 60]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [11111,22222,33333,44444,55555,66666,77777,88888,99999,111111], elements = [1,11,22,33,44,55,66,77,88,99]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100000, 50000, 25000, 12500, 6250, 3125, 1562, 781, 390], elements = [1, 2, 4, 8, 16, 32, 64, 128, 256]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [13, 26, 39, 52, 65, 78, 91], elements = [1, 13, 26, 39, 52]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [999, 1998, 2997, 3996, 4995, 5994, 6993, 7992, 8991, 9990], elements = [9, 11, 13, 17, 19, 23, 29]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [101, 202, 303, 404, 505, 606, 707, 808, 909, 1010], elements = [1, 2, 3, 4, 5]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100, 150, 200, 250, 300], elements = [50, 100, 150, 200]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50], elements = [1, 5, 10, 15, 20]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135], elements = [9, 18, 27, 36, 45]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90], elements = [9, 18, 27, 36, 45]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [101, 103, 107, 109, 113], elements = [1, 2, 3, 5, 7]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [50, 75, 100, 125, 150, 175, 200], elements = [25, 50, 100, 125]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7, 11, 13, 17, 19], elements = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10000, 20000, 30000, 40000, 50000], elements = [100, 200, 500, 1000, 2000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [60, 120, 180, 240, 300, 360, 420, 480, 540], elements = [6, 12, 18, 24, 30]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 15, 18, 21, 24], elements = [3, 4, 6, 8, 12]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100, 200, 300, 400, 500], elements = [50, 100, 250]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [24, 36, 48, 60, 72, 84, 96, 108], elements = [2, 3, 4, 6]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [210, 315, 420, 525, 630, 735], elements = [5, 7, 15, 21, 35]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10000, 20000, 30000, 40000, 50000], elements = [1000, 2000, 5000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [8, 16, 32, 64, 128, 256, 512, 1024, 2048], elements = [2, 4, 8, 16, 32]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5, 10, 15, 20, 25, 30, 35, 40], elements = [5, 10, 15]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 15, 18, 21, 24, 27, 30], elements = [3, 6, 9, 12, 15]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [101, 103, 107, 109, 113], elements = [7, 11, 13]) == [-1, -1, -1, -1, -1]

Answer: assert Solution().assignElements(groups = [33, 66, 99, 132, 165, 198, 231, 264, 297, 330], elements = [11, 22, 33, 44, 55]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10000,20000,30000,40000,50000], elements = [100,200,500,1000,2000,5000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97], elements = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]

Answer: assert Solution().assignElements(groups = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36], elements = [3, 6, 9, 12, 15]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [2, 3, 5, 7, 11, 13, 17, 19], elements = [1, 2, 3, 5, 7, 11]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [50, 25, 75, 100, 200], elements = [10, 25, 50, 100]) == [0, 1, 1, 0, 0]

Answer: assert Solution().assignElements(groups = [10000, 20000, 30000, 40000, 50000], elements = [500, 1000, 2000, 2500, 5000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [111, 222, 333, 444, 555, 666, 777, 888, 999], elements = [11, 22, 33, 44]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1]

Answer: assert Solution().assignElements(groups = [100, 200, 300, 400, 500, 600, 700, 800, 900], elements = [50, 100, 150, 200, 250]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [121, 132, 143, 154, 165], elements = [11, 22, 33, 44, 55]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [128, 256, 512, 1024, 2048, 4096, 8192, 16384], elements = [64, 128, 256]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [99, 198, 297, 396, 495], elements = [9, 18, 27, 36, 45]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7, 14, 21, 28, 35], elements = [7, 14, 21]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [111, 222, 333, 444, 555], elements = [11, 22, 33, 44, 55]) == [-1, -1, -1, -1, -1]

Answer: assert Solution().assignElements(groups = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90], elements = [3, 6, 9, 12, 15]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [97, 98, 99, 100, 101, 102, 103, 104, 105], elements = [7, 11, 13, 17]) == [-1, 0, 1, -1, -1, 3, -1, 2, 0]

Answer: assert Solution().assignElements(groups = [9, 18, 27, 36, 45], elements = [3, 9, 18, 27]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [2, 4, 8, 16, 32], elements = [2, 4, 8, 16]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [11, 22, 33, 44, 55], elements = [11, 22, 33]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [6, 12, 18, 24, 30], elements = [2, 3, 6, 12]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [3, 5, 7, 9, 11, 13, 15], elements = [3, 5, 7]) == [0, 1, 2, 0, -1, -1, 0]

Answer: assert Solution().assignElements(groups = [100, 200, 300, 400, 500, 600, 700, 800], elements = [25, 50, 100]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12345,23456,34567,45678,56789,67890,78901,89012,90123,10123], elements = [1,12,34,56,78,90,123,456,789,1012]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5, 10, 15, 20, 25, 30], elements = [5, 10, 15]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [30, 45, 60, 75, 90], elements = [15, 20, 30, 45]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [49, 70, 91, 112, 133, 154], elements = [7, 14, 21, 28, 35]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [20, 40, 60, 80, 100], elements = [10, 20, 25, 40]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5, 15, 25, 35, 45, 55], elements = [5, 15, 25, 35]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 15, 20, 25, 30], elements = [3, 5, 6, 10]) == [0, 0, 1, 1, 0]

Answer: assert Solution().assignElements(groups = [8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120], elements = [8, 16, 24, 32, 40]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 15, 20, 25, 30, 35, 40], elements = [5, 10, 15, 20]) == [-1, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [42, 84, 126, 168, 210, 252, 294, 336, 378, 420], elements = [6, 12, 14, 21, 28]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [8, 16, 24, 32, 40, 48, 56, 64, 72, 80], elements = [2, 4, 8, 16]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100000, 50000, 25000, 12500, 6250], elements = [500, 250, 125]) == [0, 0, 0, 0, 1]

Answer: assert Solution().assignElements(groups = [13, 26, 39, 52, 65], elements = [13, 26, 39]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [35, 70, 105, 140, 175], elements = [5, 7, 10, 15, 20]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [6,12,18,24,30,36,42,48,54,60], elements = [2,3,4,5,6,10,12,15,20,30]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100,101,102,103,104,105,106,107,108,109], elements = [2,3,4,5,6,7,8,9,10,11]) == [0, -1, 0, -1, 0, 1, 0, -1, 0, -1]

Answer: assert Solution().assignElements(groups = [100000, 50000, 25000, 12500, 6250, 3125, 1562, 781, 390, 195], elements = [5, 10, 25, 50, 125]) == [0, 0, 0, 0, 0, 0, -1, -1, 0, 0]

Answer: assert Solution().assignElements(groups = [42, 49, 56, 63, 70], elements = [7, 14, 21, 28]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [101, 202, 303, 404, 505, 606, 707, 808, 909, 1010], elements = [101, 202, 303, 404, 505]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [30, 45, 60, 75, 90], elements = [3, 5, 15, 30]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [20, 25, 30, 35, 40], elements = [5, 10, 15, 20]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70], elements = [7, 14, 21, 28, 35]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30], elements = [3, 6, 9, 12]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [100000, 200000, 300000, 400000, 500000], elements = [10000, 20000, 50000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [5, 10, 15, 20, 25, 30, 35], elements = [5, 10, 15, 20]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [81, 27, 9, 3, 1], elements = [1, 3, 9, 27, 81]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [24, 36, 48, 60, 72], elements = [8, 12, 24]) == [0, 1, 0, 1, 0]

Answer: assert Solution().assignElements(groups = [23, 46, 69, 92, 115, 138, 161, 184, 207, 230], elements = [23, 46, 69, 92]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [42, 84, 126, 168, 210], elements = [6, 12, 21]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 18, 24, 30, 36, 40], elements = [2, 3, 4, 5, 6, 10]) == [0, 0, 0, 0, 0, 0]

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

Answer: assert Solution().assignElements(groups = [7, 14, 21, 28, 35, 42, 49, 56], elements = [7, 14, 28]) == [0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [101, 202, 303, 404, 505, 606, 707, 808, 909], elements = [1, 101, 202, 303]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [10000, 20000, 30000, 40000, 50000], elements = [500, 1000, 2000, 5000]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [8, 12, 15, 20, 30], elements = [1, 2, 3, 4, 5]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195], elements = [13, 26, 39, 52, 65]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12,15,18,20,24,30,36], elements = [3,4,5,6,10,12]) == [0, 0, 0, 1, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 24, 36, 48, 60, 72], elements = [6, 12, 18, 24]) == [0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [8, 16, 32, 64, 128, 256, 512], elements = [2, 4, 8, 16, 32, 64]) == [0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [97,101,103,107,109], elements = [1,97,101,103,107,109]) == [0, 0, 0, 0, 0]

Answer: assert Solution().assignElements(groups = [12, 24, 36, 48, 60, 72, 84, 96, 108, 120], elements = [12, 24, 36, 48]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

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

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

inf = float('inf')

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

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

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

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

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

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

class Solution:
    def assignElements(self, groups: List[int], elements: List[int]) -> List[int]:
        mx = max(groups)
        d = [-1] * (mx + 1)
        for j, x in enumerate(elements):
            if x > mx or d[x] != -1:
                continue
            for y in range(x, mx + 1, x):
                if d[y] == -1:
                    d[y] = j
        return [d[x] for x in groups]


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

PROBLEM:
You are given a string s consisting of digits.
Return the number of substrings of s divisible by their non-zero last digit.
Note: A substring may contain leading zeros.

Example 1:

Input: s = "12936"
Output: 11
Explanation:
Substrings "29", "129", "293" and "2936" are not divisible by their last digit. There are 15 substrings in total, so the answer is 15 - 4 = 11.

Example 2:

Input: s = "5701283"
Output: 18
Explanation:
Substrings "01", "12", "701", "012", "128", "5701", "7012", "0128", "57012", "70128", "570128", and "701283" are all divisible by their last digit. Additionally, all substrings that are just 1 non-zero digit are divisible by themselves. Since there are 6 such digits, the answer is 12 + 6 = 18.

Example 3:

Input: s = "1010101010"
Output: 25
Explanation:
Only substrings that end with digit '1' are divisible by their last digit. There are 25 such substrings.

Constraints:

1 <= s.length <= 105
s consists of digits only.

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

SOLUTION:

Question:
PROBLEM:
You are given a string s consisting of digits.
Return the number of substrings of s divisible by their non-zero last digit.
Note: A substring may contain leading zeros.

Example 1:

Input: s = "12936"
Output: 11
Explanation:
Substrings "29", "129", "293" and "2936" are not divisible by their last digit. There are 15 substrings in total, so the answer is 15 - 4 = 11.

Example 2:

Input: s = "5701283"
Output: 18
Explanation:
Substrings "01", "12", "701", "012", "128", "5701", "7012", "0128", "57012", "70128", "570128", and "701283" are all divisible by their last digit. Additionally, all substrings that are just 1 non-zero digit are divisible by themselves. Since there are 6 such digits, the answer is 12 + 6 = 18.

Example 3:

Input: s = "1010101010"
Output: 25
Explanation:
Only substrings that end with digit '1' are divisible by their last digit. There are 25 such substrings.

Constraints:

1 <= s.length <= 105
s consists of digits only.

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

SOLUTION:

assert Solution().countSubstrings(s = "24680") == 6

assert Solution().countSubstrings(s = "11111") == 15

assert Solution().countSubstrings(s = "5701283") == 18

assert Solution().countSubstrings(s = "9876543210") == 35

assert Solution().countSubstrings(s = "1001001001") == 22

assert Solution().countSubstrings(s = "9999999999") == 55

assert Solution().countSubstrings(s = "1111111111") == 55

assert Solution().countSubstrings(s = "9090909090") == 25

assert Solution().countSubstrings(s = "909090909") == 25

assert Solution().countSubstrings(s = "2468024680") == 24

assert Solution().countSubstrings(s = "00000") == 0

assert Solution().countSubstrings(s = "13579") == 8

assert Solution().countSubstrings(s = "12936") == 11

assert Solution().countSubstrings(s = "1010101010") == 25

assert Solution().countSubstrings(s = "1234567890") == 20

assert Solution().countSubstrings(s = "0000000000") == 0

assert Solution().countSubstrings(s = "1100110011001100") == 60

assert Solution().countSubstrings(s = "5678901234") == 28

assert Solution().countSubstrings(s = "246802468024680") == 52

assert Solution().countSubstrings(s = "909090909090909") == 64

assert Solution().countSubstrings(s = "2222222222") == 55

assert Solution().countSubstrings(s = "999000999000999000") == 72

assert Solution().countSubstrings(s = "102030405060708090") == 39

assert Solution().countSubstrings(s = "123123123123123") == 105

Answer: assert Solution().countSubstrings(s = "24680") == 6

Answer: assert Solution().countSubstrings(s = "11111") == 15

Answer: assert Solution().countSubstrings(s = "5701283") == 18

Answer: assert Solution().countSubstrings(s = "9876543210") == 35

Answer: assert Solution().countSubstrings(s = "1001001001") == 22

Answer: assert Solution().countSubstrings(s = "9999999999") == 55

Answer: assert Solution().countSubstrings(s = "1111111111") == 55

Answer: assert Solution().countSubstrings(s = "9090909090") == 25

Answer: assert Solution().countSubstrings(s = "909090909") == 25

Answer: assert Solution().countSubstrings(s = "2468024680") == 24

Answer: assert Solution().countSubstrings(s = "00000") == 0

Answer: assert Solution().countSubstrings(s = "13579") == 8

Answer: assert Solution().countSubstrings(s = "12936") == 11

Answer: assert Solution().countSubstrings(s = "1010101010") == 25

Answer: assert Solution().countSubstrings(s = "12345678901234567890") == 88

Answer: assert Solution().countSubstrings(s = "1234567890") == 20

Answer: assert Solution().countSubstrings(s = "0000000000") == 0

Answer: assert Solution().countSubstrings(s = "11111222223333344444") == 160

Answer: assert Solution().countSubstrings(s = "13579135791357913579") == 118

Answer: assert Solution().countSubstrings(s = "1234512345123451234512345123451234512345123451234512345") == 1111

Answer: assert Solution().countSubstrings(s = "7777777777777777777777777777777") == 496

Answer: assert Solution().countSubstrings(s = "001001001001001001001001001001001001001001001001") == 408

Answer: assert Solution().countSubstrings(s = "12345678901234567890123456789012345678901234567890") == 587

Answer: assert Solution().countSubstrings(s = "123456789000000000001234567890") == 148

Answer: assert Solution().countSubstrings(s = "54321098765432109876543210") == 190

Answer: assert Solution().countSubstrings(s = "123456789123456789123456789123456789123456789") == 522

Answer: assert Solution().countSubstrings(s = "98765432101234567890") == 104

Answer: assert Solution().countSubstrings(s = "1100110011001100") == 60

Answer: assert Solution().countSubstrings(s = "123456789011121314151617181920212223242526272829303132333435363738394041424344454647484950") == 2238

Answer: assert Solution().countSubstrings(s = "111112222233333444445555566666777778888899999") == 550

Answer: assert Solution().countSubstrings(s = "010010001000010000010000001000000001000000000100000000001") == 216

Answer: assert Solution().countSubstrings(s = "0102030405060708090102030405") == 158

Answer: assert Solution().countSubstrings(s = "52525252525252525252") == 210

Answer: assert Solution().countSubstrings(s = "25025025025025025025025025") == 243

Answer: assert Solution().countSubstrings(s = "10000000000000000000") == 1

Answer: assert Solution().countSubstrings(s = "86420864208642086420") == 133

Answer: assert Solution().countSubstrings(s = "2222222222222222222") == 190

Answer: assert Solution().countSubstrings(s = "0000000000000000000000000000000") == 0

Answer: assert Solution().countSubstrings(s = "12300000000000000000") == 5

Answer: assert Solution().countSubstrings(s = "123456789098765432101234567890") == 220

Answer: assert Solution().countSubstrings(s = "1001001001001001001001001001001") == 176

Answer: assert Solution().countSubstrings(s = "00000000001234567890") == 80

Answer: assert Solution().countSubstrings(s = "135791113151719212325") == 184

Answer: assert Solution().countSubstrings(s = "78945612307894561230") == 117

Answer: assert Solution().countSubstrings(s = "12345999999999999999") == 146

Answer: assert Solution().countSubstrings(s = "12034567890123456789") == 95

Answer: assert Solution().countSubstrings(s = "5678901234") == 28

Answer: assert Solution().countSubstrings(s = "01234567890123456789") == 101

Answer: assert Solution().countSubstrings(s = "99999999999999999999") == 210

Answer: assert Solution().countSubstrings(s = "505050505050505050505050505050") == 225

Answer: assert Solution().countSubstrings(s = "11111111111111111111") == 210

Answer: assert Solution().countSubstrings(s = "11223344556677889900") == 71

Answer: assert Solution().countSubstrings(s = "10000000010000000010") == 30

Answer: assert Solution().countSubstrings(s = "246802468024680") == 52

Answer: assert Solution().countSubstrings(s = "100000000010000000001000000000") == 33

Answer: assert Solution().countSubstrings(s = "12345678901112131415161718192021222324252627282930") == 898

Answer: assert Solution().countSubstrings(s = "36912580473691258047") == 119

Answer: assert Solution().countSubstrings(s = "3330333033303330333") == 150

Answer: assert Solution().countSubstrings(s = "987654321987654321987654321987654321987654321") == 603

Answer: assert Solution().countSubstrings(s = "86420864208642086420864208642086420") == 407

Answer: assert Solution().countSubstrings(s = "9876543210987654321098765432109876543210") == 435

Answer: assert Solution().countSubstrings(s = "98765432109876543210") == 119

Answer: assert Solution().countSubstrings(s = "24681357902468135790") == 110

Answer: assert Solution().countSubstrings(s = "123456789876543210123456789") == 193

Answer: assert Solution().countSubstrings(s = "111111111122222222223333333333") == 335

Answer: assert Solution().countSubstrings(s = "98765432100000000001") == 55

Answer: assert Solution().countSubstrings(s = "111222333444555666777888999") == 183

Answer: assert Solution().countSubstrings(s = "10010010010010010010") == 70

Answer: assert Solution().countSubstrings(s = "50505050505050505050") == 100

Answer: assert Solution().countSubstrings(s = "1001001001001001001001") == 92

Answer: assert Solution().countSubstrings(s = "987654321987654321987654321") == 233

Answer: assert Solution().countSubstrings(s = "112233445566778899001122334455667788990011223344") == 612

Answer: assert Solution().countSubstrings(s = "24680246802468024680") == 93

Answer: assert Solution().countSubstrings(s = "99999888887777766666") == 120

Answer: assert Solution().countSubstrings(s = "258025802580258025802580258025802580258025802580") == 576

Answer: assert Solution().countSubstrings(s = "909090909090909") == 64

Answer: assert Solution().countSubstrings(s = "09090909090909090909") == 110

Answer: assert Solution().countSubstrings(s = "98765432109876543210987654321098765432109876543210") == 667

Answer: assert Solution().countSubstrings(s = "1001001001001001001") == 70

Answer: assert Solution().countSubstrings(s = "12345678909876543210") == 104

Answer: assert Solution().countSubstrings(s = "987654321000000000000000000000") == 35

Answer: assert Solution().countSubstrings(s = "12213332211221333221") == 174

Answer: assert Solution().countSubstrings(s = "1110001110001110001") == 91

Answer: assert Solution().countSubstrings(s = "2222222222") == 55

Answer: assert Solution().countSubstrings(s = "55555555555555555555") == 210

Answer: assert Solution().countSubstrings(s = "123012301230123012301230") == 195

Answer: assert Solution().countSubstrings(s = "123455432112345543211234554321") == 342

Answer: assert Solution().countSubstrings(s = "12345098765432109876") == 101

Answer: assert Solution().countSubstrings(s = "00000000000000000000") == 0

Answer: assert Solution().countSubstrings(s = "13579246801357924680135792468013579246801357924680") == 691

Answer: assert Solution().countSubstrings(s = "999000999000999000") == 72

Answer: assert Solution().countSubstrings(s = "10101010101010101010101010101010101010101010") == 484

Answer: assert Solution().countSubstrings(s = "13579246801357924680") == 109

Answer: assert Solution().countSubstrings(s = "987654321098765432109876543210") == 252

Answer: assert Solution().countSubstrings(s = "50505050505050505050505") == 144

Answer: assert Solution().countSubstrings(s = "8642086420864208642086420864208642086420864208642086420") == 1005

Answer: assert Solution().countSubstrings(s = "101010101010101010101010101010101010101010101010") == 576

Answer: assert Solution().countSubstrings(s = "987654321011121314151617181920") == 316

Answer: assert Solution().countSubstrings(s = "36936936936936936936") == 189

Answer: assert Solution().countSubstrings(s = "5050505050505050505050") == 121

Answer: assert Solution().countSubstrings(s = "2468024680246802468024680") == 146

Answer: assert Solution().countSubstrings(s = "98765432101111111111") == 190

Answer: assert Solution().countSubstrings(s = "123321123321123321123321") == 268

Answer: assert Solution().countSubstrings(s = "44444444444444444444444444") == 351

Answer: assert Solution().countSubstrings(s = "123412341234123412341234123412341234123412341234") == 680

Answer: assert Solution().countSubstrings(s = "1100110011001100110011") == 138

Answer: assert Solution().countSubstrings(s = "102030405060708090") == 39

Answer: assert Solution().countSubstrings(s = "1212121212121212121") == 190

Answer: assert Solution().countSubstrings(s = "9090909090909090909") == 100

Answer: assert Solution().countSubstrings(s = "12345678900000000000") == 20

Answer: assert Solution().countSubstrings(s = "123123123123123") == 105

Answer: assert Solution().countSubstrings(s = "10101010101010101010") == 100

Answer: assert Solution().countSubstrings(s = "123456789012345678901234567890") == 205

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 countSubstrings(self, s: str) -> int:
    ans = 0
    # dp[i][num][rem] := the number of first `i` digits of s that have a
    # remainder of `rem` when divided by `num`
    dp = [[[0] * 10 for _ in range(10)] for _ in range(len(s) + 1)]

    for i in range(1, len(s) + 1):
      digit = int(s[i - 1])
      for num in range(1, 10):
        for rem in range(num):
          dp[i][num][(rem * 10 + digit) % num] += dp[i - 1][num][rem]
        dp[i][num][digit % num] += 1
      ans += dp[i][digit][0]

    return ans