input: from typing import List
  
  
  def lcs(X: str, Y: str) -> int:
      """
      Given two strings X and Y, find the length of the longest common subsequence between them.
      >>> lcs("ABACEDF", "ABDCF")
      4
      >>> lcs("ABCBDAB", "BDCAB")
      4
      """
      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])
  
      return L[m][n]
output:     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])
  
      return L[m][n]