input: Write a python function to find the longest common subsequence (LCS) of two strings.
  assert lcs("ABCDGH", "AEDFHR") == "ADH"
  assert lcs("AGGTAB", "GXTXAYB") == "GTAB"
  assert lcs("ABC", "AC") == "AC"
output: def lcs(X, Y):
      m = len(X)
      n = len(Y)
      L = [[None] * (n + 1) for i in range(m + 1)]
      
      for i in range(m + 1):
          for j in range(n + 1):
              if i == 0 or j == 0:
                  L[i][j] = 0
              elif X[i-1] == Y[j-1]:
                  L[i][j] = L[i-1][j-1] + 1
              else:
                  L[i][j] = max(L[i-1][j], L[i][j-1])
      
      index = L[m][n]
      lcs = [""] * (index + 1)
      lcs[index] = ""
      
      i = m
      j = n
      while i > 0 and j > 0:
          if X[i-1] == Y[j-1]:
              lcs[index-1] = X[i-1]
              i -= 1
              j -= 1
              index -= 1
          elif L[i-1][j] > L[i][j-1]:
              i -= 1
          else:
              j -= 1
      
      return "".join(lcs)