import math

class Solution:
  def countMinJumps(self, jumps):

    def dp(index, count, memo):
      
      if (index, count) in memo:
        return memo[(index, count)]

      if index >= len(jumps) - 1:
        return count

      min_count = float('inf')
      
      for i in range(index + 1, index + jumps[index] + 1):
        min_count = min(dp(i, count + 1, memo), min_count)

      memo[(index, count)] = min_count

      return min_count

    return dp(0, 0, {})