input: 
  def longest_common_subsequence(string1: str, string2: str) -> int:
      """ Find the length of the longest common subsequence between two strings.
      >>> longest_common_subsequence("ABACEDF", "ABDCF")
      4
      >>> longest_common_subsequence("ABC", "AC")
      2
      """
  
output:     dp = [[0] * (len(string2) + 1) for _ in range(len(string1) + 1)]
      
      for i in range(1, len(string1) + 1):
          for j in range(1, len(string2) + 1):
              if string1[i - 1] == string2[j - 1]:
                  dp[i][j] = dp[i - 1][j - 1] + 1
              else:
                  dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
      
      return dp[-1][-1]