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 36 terminals, ranging from 1 to 36.
Each terminal symbol occurs in the target sequence at least once.

There are 75 non-terminal symbols, ranging from A1 to A75.

Production rules:
rule_1: A1 -> A2
rule_2: A2 -> A74 A75 A73
rule_3: A3 -> A4 A5
rule_4: A4 -> 7
rule_5: A5 -> 5 A6
rule_6: A5 -> 6 A7
rule_7: A6 -> 1
rule_8: A6 -> 2
rule_9: A6 -> 3
rule_10: A6 -> 4
rule_11: A7 -> 1
rule_12: A7 -> 2
rule_13: A7 -> 3
rule_14: A7 -> 4
rule_15: A8 -> A9 A10
rule_16: A9 -> 8
rule_17: A10 -> 5 A11
rule_18: A10 -> 6 A12
rule_19: A11 -> 1
rule_20: A11 -> 2
rule_21: A11 -> 3
rule_22: A11 -> 4
rule_23: A12 -> 1
rule_24: A12 -> 2
rule_25: A12 -> 3
rule_26: A12 -> 4
rule_27: A13 -> A14 A15
rule_28: A14 -> 14
rule_29: A15 -> 12 A16
rule_30: A15 -> 13 A17
rule_31: A16 -> 1
rule_32: A16 -> 2
rule_33: A16 -> 3
rule_34: A16 -> 4
rule_35: A17 -> 1
rule_36: A17 -> 2
rule_37: A17 -> 3
rule_38: A17 -> 4
rule_39: A18 -> A19 A20
rule_40: A19 -> 15
rule_41: A20 -> 12 A21
rule_42: A20 -> 13 A22
rule_43: A21 -> 1
rule_44: A21 -> 2
rule_45: A21 -> 3
rule_46: A21 -> 4
rule_47: A21 -> 16
rule_48: A22 -> 1
rule_49: A22 -> 2
rule_50: A22 -> 3
rule_51: A22 -> 4
rule_52: A23 -> A24 A25
rule_53: A24 -> 17
rule_54: A25 -> 19 A26
rule_55: A25 -> 20 A27
rule_56: A26 -> 1
rule_57: A26 -> 2
rule_58: A26 -> 3
rule_59: A26 -> 4
rule_60: A26 -> 18
rule_61: A27 -> 1
rule_62: A27 -> 2
rule_63: A27 -> 3
rule_64: A27 -> 4
rule_65: A28 -> A29 A30
rule_66: A29 -> 21
rule_67: A30 -> 19 A31
rule_68: A30 -> 20 A32
rule_69: A31 -> 1
rule_70: A31 -> 2
rule_71: A31 -> 3
rule_72: A31 -> 4
rule_73: A32 -> 1
rule_74: A32 -> 2
rule_75: A32 -> 3
rule_76: A32 -> 4
rule_77: A33 -> 10 A34
rule_78: A34 -> 1
rule_79: A34 -> 2
rule_80: A34 -> 3
rule_81: A34 -> 4
rule_82: A34 -> 22
rule_83: A35 -> A36 A33
rule_84: A36 -> 23
rule_85: A37 -> 24 A35
rule_86: A37 -> A38
rule_87: A37 -> A39
rule_88: A37 -> A40
rule_89: A37 -> A41
rule_90: A37 -> A42
rule_91: A37 -> A43
rule_92: A37 -> A44
rule_93: A37 -> A45
rule_94: A37 -> A46
rule_95: A37 -> A47
rule_96: A37 -> A48
rule_97: A37 -> A49
rule_98: A38 -> 9
rule_99: A39 -> 9
rule_100: A40 -> 9
rule_101: A41 -> 9
rule_102: A42 -> 9
rule_103: A43 -> 9
rule_104: A44 -> 9
rule_105: A45 -> 9
rule_106: A46 -> 9
rule_107: A47 -> 9
rule_108: A48 -> 9
rule_109: A49 -> 9
rule_110: A50 -> 26 A51
rule_111: A51 -> 11
rule_112: A51 -> 27
rule_113: A52 -> A53
rule_114: A52 -> A54
rule_115: A52 -> A55
rule_116: A52 -> A56
rule_117: A52 -> A57
rule_118: A52 -> A58
rule_119: A52 -> A59
rule_120: A52 -> A60
rule_121: A52 -> A61
rule_122: A52 -> A62
rule_123: A52 -> A63
rule_124: A52 -> A64
rule_125: A53 -> 9
rule_126: A54 -> 9
rule_127: A55 -> 9
rule_128: A56 -> 9
rule_129: A57 -> 9
rule_130: A58 -> 9
rule_131: A59 -> 9
rule_132: A60 -> 9
rule_133: A61 -> 9
rule_134: A62 -> 9
rule_135: A63 -> 9
rule_136: A64 -> 9
rule_137: A65 -> 28 A66
rule_138: A66 -> 11
rule_139: A67 -> A68 A65 A3 A52
rule_140: A68 -> 29 A8
rule_141: A69 -> A70 A50 A23 A37
rule_142: A70 -> 30 A28
rule_143: A71 -> 32
rule_144: A72 -> 32
rule_145: A73 -> A69
rule_146: A74 -> A67 A71
rule_147: A74 -> A69 A72
rule_148: A75 -> 34 A13 A13 35
rule_149: A75 -> 34 A13 A18 35

Target sequence:
29 8 6 1 28 11 7 5 2 9 32 33 34 14 13 3 36 15 12 16 35 30 21 20 4 26 27 17 19 18 24 23 10 22 25 31
"""