input: def longest_common_subsequence(string1: str, string2: str) -> str:
      """
      Finds the longest common subsequence between two given strings.
      
      >>> longest_common_subsequence("ABCDF", "ABECD")
      'ABCD'
      """
output:     m, n = len(string1), len(string2)
      dp = [["" for _ in range(n + 1)] for _ in range(m + 1)]
      
      for i in range(1, m + 1):
          for j in range(1, n + 1):
              if string1[i - 1] == string2[j - 1]:
                  dp[i][j] = dp[i - 1][j - 1] + string1[i - 1]
              else:
                  dp[i][j] = max(dp[i - 1][j], dp[i][j - 1], key=len)
      
      return dp[m][n]