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 34 terminals, ranging from 1 to 34.
Each terminal symbol occurs in the target sequence at least once.

There are 70 non-terminal symbols, ranging from A1 to A70.

Production rules:
rule_1: A1 -> A2
rule_2: A2 -> 33 A60 A58 A62 A3 A3 A61 A60
rule_3: A2 -> 33 A60 A58 A64 A3 A3 31 A63 A60
rule_4: A2 -> 33 A60 A58 A66 A3 32 A3 31 A65 30 A60
rule_5: A2 -> 33 A60 A58 A68 A3 32 A3 31 A67 30 A60
rule_6: A2 -> 33 A60 A58 A70 A3 A3 31 A69 30 A60
rule_7: A3 -> A4 A5
rule_8: A3 -> 6
rule_9: A4 -> 7
rule_10: A5 -> 5 A6
rule_11: A6 -> 1
rule_12: A6 -> 2
rule_13: A6 -> 8
rule_14: A7 -> A8 A9
rule_15: A8 -> 12
rule_16: A9 -> 9 A10
rule_17: A9 -> 10 A11
rule_18: A9 -> 11 A12
rule_19: A10 -> 1
rule_20: A10 -> 2
rule_21: A10 -> 13
rule_22: A11 -> 1
rule_23: A11 -> 2
rule_24: A12 -> 1
rule_25: A12 -> 2
rule_26: A13 -> A14 A15
rule_27: A14 -> 14
rule_28: A15 -> 9 A16
rule_29: A15 -> 10 A17
rule_30: A15 -> 11 A18
rule_31: A16 -> 1
rule_32: A16 -> 2
rule_33: A17 -> 1
rule_34: A17 -> 2
rule_35: A18 -> 1
rule_36: A18 -> 2
rule_37: A18 -> 15
rule_38: A19 -> A20 A21
rule_39: A20 -> 17
rule_40: A21 -> 16 A22
rule_41: A22 -> 1
rule_42: A22 -> 2
rule_43: A23 -> 18
rule_44: A24 -> A25
rule_45: A24 -> A26
rule_46: A24 -> A27
rule_47: A24 -> A28
rule_48: A24 -> A29
rule_49: A24 -> A30
rule_50: A24 -> A31
rule_51: A24 -> A32
rule_52: A24 -> A33
rule_53: A24 -> A34
rule_54: A24 -> A35
rule_55: A24 -> A36
rule_56: A25 -> 3
rule_57: A26 -> 3
rule_58: A27 -> 3
rule_59: A28 -> 3
rule_60: A29 -> 3
rule_61: A30 -> 3
rule_62: A31 -> 3
rule_63: A32 -> 3
rule_64: A33 -> 3
rule_65: A34 -> 3
rule_66: A35 -> 3
rule_67: A36 -> 3
rule_68: A37 -> 19 A38
rule_69: A38 -> 4
rule_70: A39 -> A40
rule_71: A39 -> A41
rule_72: A39 -> A42
rule_73: A39 -> A43
rule_74: A39 -> A44
rule_75: A39 -> A45
rule_76: A39 -> A46
rule_77: A39 -> A47
rule_78: A39 -> A48
rule_79: A39 -> A49
rule_80: A39 -> A50
rule_81: A39 -> A51
rule_82: A40 -> 3
rule_83: A41 -> 3
rule_84: A42 -> 3
rule_85: A43 -> 3
rule_86: A44 -> 3
rule_87: A45 -> 3
rule_88: A46 -> 3
rule_89: A47 -> 3
rule_90: A47 -> 20
rule_91: A48 -> 3
rule_92: A49 -> 3
rule_93: A50 -> 3
rule_94: A51 -> 3
rule_95: A52 -> 21 A53
rule_96: A53 -> 4
rule_97: A53 -> 22
rule_98: A54 -> A55 A52 A13 A39
rule_99: A55 -> 23 A7
rule_100: A56 -> A57 A37 A19 A24
rule_101: A57 -> 24 A23
rule_102: A58 -> A59 A15
rule_103: A59 -> 25
rule_104: A60 -> 26
rule_105: A60 -> 29
rule_106: A61 -> A54 27
rule_107: A62 -> A56 28
rule_108: A63 -> A54
rule_109: A64 -> A54
rule_110: A64 -> A56 28
rule_111: A65 -> A54 27
rule_112: A65 -> A56
rule_113: A66 -> A56
rule_114: A67 -> A54 27
rule_115: A67 -> A58
rule_116: A68 -> A54
rule_117: A68 -> A56 28
rule_118: A68 -> A58
rule_119: A69 -> A54
rule_120: A69 -> A58
rule_121: A70 -> A56 28

Target sequence:
33 26 25 10 1 24 18 19 4 17 16 2 3 28 7 5 8 32 34 6 31 23 12 9 13 21 22 14 11 15 20 27 30 29
"""