I have a context free grammar (CFG). The initial symbol is `A1`. The terminal symbols are just integers and the non-terminal symbols start with `A`. I also have a target sequence of terminal symbols which needs to be produced by the grammar. However, the CFG production rules have had some terminal symbols removed which may now render it impossible to produce the target sequence. Please attempt to repair the CFG so that the sequence can be produced. The only operations which can be made to repair the CFG are the insertion of terminal symbols anywhere in existing production rules. Deleting or reordering symbols in existing production rules and creating new production rules is prohibited. Please try minimize the total number of terminal symbols inserted into the production rules so that the CFG can produce the target sequence. Reason about the problem however you wish and write out whatever working out you want. When you are finished please write a new line with `Updated production rules:`, and then write a new line for each of the updated production rules (including `rule_<n>:`), no need to rewrite the production rules which haven't changed. Do not write anything after the updated production rules.


"""
There are 29 terminals, ranging from 1 to 29.
Each terminal symbol occurs in the target sequence at least once.

There are 39 non-terminal symbols, ranging from A1 to A39.

Production rules:
rule_1: A1 -> A32 A24 A15 A2
rule_2: A2 -> 1
rule_3: A2 -> 1 A3 A10
rule_4: A2 -> 1 A7 A11 3
rule_5: A2 -> A8 A7
rule_6: A2 -> A14 A7 4 3
rule_7: A3 -> 1
rule_8: A3 -> 1 A4
rule_9: A4 -> A5
rule_10: A5 -> 1
rule_11: A5 -> 2
rule_12: A6 -> 1
rule_13: A7 -> 1
rule_14: A8 -> 1
rule_15: A8 -> 5
rule_16: A8 -> 6
rule_17: A9 -> 1
rule_18: A9 -> 7
rule_19: A10 -> A5
rule_20: A10 -> A6
rule_21: A11 -> A8 4
rule_22: A12 -> A13
rule_23: A12 -> A13
rule_24: A13 -> 1
rule_25: A13 -> 10
rule_26: A14 -> A12 5
rule_27: A15 -> 1
rule_28: A15 -> A7 A16 A21
rule_29: A15 -> A8 A16 11
rule_30: A15 -> A9 A16 11
rule_31: A15 -> A22 A16 11
rule_32: A16 -> 1
rule_33: A16 -> A7 A17
rule_34: A16 -> A19 12 A18
rule_35: A17 -> A9
rule_36: A18 -> A8
rule_37: A18 -> A9 13
rule_38: A19 -> 1
rule_39: A19 -> 1 A20
rule_40: A20 -> A8 15
rule_41: A20 -> A9
rule_42: A21 -> A8 16
rule_43: A22 -> A23 6
rule_44: A23 -> A5 A3 17
rule_45: A23 -> A5 A3 18
rule_46: A24 -> 1
rule_47: A24 -> 1 A25 A29
rule_48: A24 -> A27 A25 19
rule_49: A24 -> A30 A25 19
rule_50: A25 -> 1
rule_51: A25 -> 1 22 A28
rule_52: A26 -> 1
rule_53: A27 -> 1
rule_54: A27 -> 21
rule_55: A28 -> A26
rule_56: A28 -> A27 23
rule_57: A29 -> A26
rule_58: A29 -> A27
rule_59: A30 -> A31
rule_60: A31 -> A9 A19
rule_61: A31 -> A9 A19 13
rule_62: A32 -> 1
rule_63: A32 -> 1 A33 A37 24
rule_64: A32 -> A34 A33 25
rule_65: A32 -> A35 A33
rule_66: A32 -> A38 A33 25 24
rule_67: A33 -> 1
rule_68: A33 -> 1 28 A36
rule_69: A34 -> 1
rule_70: A34 -> 26
rule_71: A35 -> 1
rule_72: A35 -> 27
rule_73: A36 -> A35
rule_74: A37 -> A34 25
rule_75: A38 -> A39 26
rule_76: A39 -> A8 1
rule_77: A39 -> A8 1 15

Target sequence:
6 1 14 15 26 1 28 27 29 25 24 7 1 12 13 21 1 22 1 23 20 19 2 1 18 17 6 1 16 11 10 1 8 9 5 1 4 3
"""