from typing import List
class Solution:
    def minHeightShelves(self, b: List[List[int]], w: int) -> int:
        print(f'Books: {b}\nShelf width: {w}')
        n = len(b)
        dp = [float('inf')] * (n + 1)
        dp[0] = 0
        print(f'initial dp: {dp}')
        for i in range(n):
            print()
            print('-' * 80)
            print(f'[{i+1} books] to consider: {b[:i+1]}')
            j = i
            width = 0
            h = 0
            while j >= 0:
                print(f'place [{j}]-th book: {b[j]}')
                width += b[j][0]
                if width > w:
                    print('The total width is beyond the shelf')
                    break
                print(f'The maximum height is updated from [{h}] to [{max(h, b[j][1])}]')
                h = max(h, b[j][1])
                
                print(f'The minimum total height for [{i+1} books] is update from [{dp[i + 1]}] to [{min(dp[i + 1], dp[j] + h)}]')
                dp[i + 1] = min(dp[i + 1], dp[j] + h)
                j -= 1
        return dp[-1]