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 47 terminals, ranging from 1 to 47.
Each terminal symbol occurs in the target sequence at least once.

There are 95 non-terminal symbols, ranging from A1 to A95.

Production rules:
rule_1: A1 -> A2
rule_2: A2 -> 47 A90 A93
rule_3: A3 -> A4 A5
rule_4: A4 -> 6
rule_5: A5 -> 4 A6
rule_6: A5 -> 5 A7
rule_7: A6 -> 1
rule_8: A6 -> 2
rule_9: A6 -> 3
rule_10: A6 -> 7
rule_11: A7 -> 1
rule_12: A7 -> 2
rule_13: A7 -> 3
rule_14: A8 -> A9 A10
rule_15: A9 -> 8
rule_16: A10 -> 4 A11
rule_17: A10 -> 5 A12
rule_18: A11 -> 1
rule_19: A11 -> 2
rule_20: A11 -> 3
rule_21: A12 -> 1
rule_22: A12 -> 2
rule_23: A12 -> 3
rule_24: A13 -> A14 A15
rule_25: A14 -> 16
rule_26: A15 -> 14 A16
rule_27: A15 -> 15 A17
rule_28: A16 -> 1
rule_29: A16 -> 2
rule_30: A16 -> 3
rule_31: A17 -> 1
rule_32: A17 -> 2
rule_33: A17 -> 3
rule_34: A18 -> A19 A20
rule_35: A19 -> 17
rule_36: A20 -> 14 A21
rule_37: A20 -> 15 A22
rule_38: A21 -> 1
rule_39: A21 -> 2
rule_40: A21 -> 3
rule_41: A22 -> 1
rule_42: A22 -> 2
rule_43: A22 -> 3
rule_44: A23 -> A24 A25
rule_45: A24 -> 18
rule_46: A25 -> 10 A26
rule_47: A25 -> 11 A27
rule_48: A25 -> 12 A28
rule_49: A26 -> 1
rule_50: A26 -> 2
rule_51: A26 -> 3
rule_52: A27 -> 1
rule_53: A27 -> 2
rule_54: A27 -> 3
rule_55: A27 -> 19
rule_56: A28 -> 1
rule_57: A28 -> 2
rule_58: A28 -> 3
rule_59: A29 -> A30 A31
rule_60: A30 -> 20
rule_61: A30 -> 21
rule_62: A31 -> 10 A32
rule_63: A31 -> 11 A33
rule_64: A31 -> 12 A34
rule_65: A32 -> 1
rule_66: A32 -> 2
rule_67: A32 -> 3
rule_68: A32 -> 22
rule_69: A33 -> 1
rule_70: A33 -> 2
rule_71: A33 -> 3
rule_72: A34 -> 1
rule_73: A34 -> 2
rule_74: A34 -> 3
rule_75: A34 -> 23
rule_76: A35 -> 24
rule_77: A36 -> 25
rule_78: A37 -> 26
rule_79: A38 -> 27
rule_80: A39 -> 28 A37
rule_81: A39 -> A40
rule_82: A39 -> A41
rule_83: A39 -> A42
rule_84: A39 -> A43
rule_85: A39 -> A44
rule_86: A39 -> A45
rule_87: A39 -> A46
rule_88: A39 -> A47
rule_89: A39 -> A48
rule_90: A39 -> A49
rule_91: A39 -> A50
rule_92: A39 -> A51
rule_93: A40 -> 9
rule_94: A41 -> 9
rule_95: A42 -> 9
rule_96: A43 -> 9
rule_97: A44 -> 9
rule_98: A45 -> 9
rule_99: A46 -> 9
rule_100: A47 -> 9
rule_101: A48 -> 9
rule_102: A49 -> 9
rule_103: A50 -> 9
rule_104: A51 -> 9
rule_105: A52 -> 30 A38
rule_106: A53 -> 33 A38 32
rule_107: A54 -> A55
rule_108: A54 -> A56
rule_109: A54 -> A57
rule_110: A54 -> A58
rule_111: A54 -> A59
rule_112: A54 -> A60
rule_113: A54 -> A61
rule_114: A54 -> A62
rule_115: A54 -> A63
rule_116: A54 -> A64
rule_117: A54 -> A65
rule_118: A54 -> A66
rule_119: A55 -> 9
rule_120: A56 -> 9
rule_121: A57 -> 9
rule_122: A58 -> 9
rule_123: A59 -> 9
rule_124: A60 -> 9
rule_125: A61 -> 9
rule_126: A62 -> 9
rule_127: A63 -> 9
rule_128: A64 -> 9
rule_129: A65 -> 9
rule_130: A66 -> 9
rule_131: A67 -> 34 A68
rule_132: A68 -> 13
rule_133: A69 -> 35 A36 36
rule_134: A69 -> A70
rule_135: A69 -> A71
rule_136: A69 -> A72
rule_137: A69 -> A73
rule_138: A69 -> A74
rule_139: A69 -> A75
rule_140: A69 -> A76
rule_141: A69 -> A77
rule_142: A69 -> A78
rule_143: A69 -> A79
rule_144: A69 -> A80
rule_145: A69 -> A81
rule_146: A70 -> 9
rule_147: A71 -> 9
rule_148: A72 -> 9
rule_149: A73 -> 9
rule_150: A74 -> 9
rule_151: A75 -> 9
rule_152: A76 -> 9
rule_153: A77 -> 9
rule_154: A78 -> 9
rule_155: A79 -> 9
rule_156: A80 -> 9
rule_157: A81 -> 9
rule_158: A82 -> 37 A83
rule_159: A83 -> 13
rule_160: A83 -> 38
rule_161: A84 -> A85 A67 A13 A54
rule_162: A85 -> 39 A18
rule_163: A86 -> A87 A82 A3 A69
rule_164: A87 -> 40 A8
rule_165: A88 -> 41 A84
rule_166: A89 -> 43 A86
rule_167: A90 -> A91
rule_168: A91 -> A92 A53 A52 A29 A39
rule_169: A92 -> 45 A35
rule_170: A93 -> A94
rule_171: A94 -> A95 A89 A29 A88
rule_172: A95 -> 46 A23

Target sequence:
47 45 24 33 27 32 30 27 31 21 12 23 28 26 29 46 18 11 19 43 40 8 5 1 37 38 6 4 7 35 25 36 44 20 10 22 41 39 17 15 2 34 13 16 14 3 9 42
"""