You are given a context free grammar G and a string S. Find the minimum Levenshtein distance between S and any string W accepted by G.   The first line of the input contains two space-separated integers Vand R denoting the number of non-terminals and the number of productions of G The following R lines describe productions. Each line starts with an integer Tdenoting the production type. If T=0, a space and three space-separated integers X, Yand Z denoting a production X→YZ If T=1, a space, an integer X, another space and a character cdenoting a production X→c If T=2, a space and a single integer X denoting a production X→ε The next line contains a single integer ST denoting the starting symbol of G. Last line contains the string S as explained in statement. Input: 5 7 0 0 1 2 0 0 3 4 2 0 1 1 a 1 3 b 0 4 0 3 0 2 0 1 0 ababb Output: 2

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You are given a context free grammar G and a string S. Find the minimum Levenshtein distance between S and any string W accepted by G.

 

  • The first line of the input contains two space-separated integers Vand R denoting the number of non-terminals and the number of productions of G
  • The following R lines describe productions.
    • Each line starts with an integer Tdenoting the production type.
    • If T=0, a space and three space-separated integers X, Yand Z denoting a production X→YZ
    • If T=1, a space, an integer X, another space and a character cdenoting a production X→c
    • If T=2, a space and a single integer X denoting a production X→ε
  • The next line contains a single integer ST denoting the starting symbol of G.
  • Last line contains the string S as explained in statement.

Input:

5 7

0 0 1 2

0 0 3 4

2 0

1 1 a

1 3 b

0 4 0 3

0 2 0 1

0

ababb

Output:

2

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