input: def lcs(X, Y):
      """ Find the longest common subsequence (LCS) between two strings.
      Example:
      >>> lcs("ABACEDF", "ABDCF")
      4
      """
output:     m = len(X)
      n = len(Y)
      dp = [[0] * (n + 1) for _ in range(m + 1)]
      
      for i in range(1, m + 1):
          for j in range(1, n + 1):
              if X[i - 1] == Y[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[m][n]