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 65 non-terminal symbols, ranging from A1 to A65.

Production rules:
rule_1: A1 -> A2
rule_2: A2 -> 36 A65 A54 A55 A56 A64
rule_3: A3 -> 6 A4
rule_4: A4 -> 1
rule_5: A4 -> 2
rule_6: A4 -> 3
rule_7: A4 -> 4
rule_8: A4 -> 5
rule_9: A5 -> A6 A7
rule_10: A6 -> 11
rule_11: A7 -> 9 A8
rule_12: A7 -> 10 A9
rule_13: A8 -> 1
rule_14: A8 -> 2
rule_15: A8 -> 3
rule_16: A8 -> 4
rule_17: A8 -> 5
rule_18: A9 -> 1
rule_19: A9 -> 2
rule_20: A9 -> 3
rule_21: A9 -> 4
rule_22: A9 -> 5
rule_23: A10 -> A11 A12
rule_24: A11 -> 12
rule_25: A12 -> 9 A13
rule_26: A12 -> 10 A14
rule_27: A13 -> 1
rule_28: A13 -> 2
rule_29: A13 -> 3
rule_30: A13 -> 4
rule_31: A13 -> 5
rule_32: A14 -> 1
rule_33: A14 -> 2
rule_34: A14 -> 3
rule_35: A14 -> 4
rule_36: A14 -> 5
rule_37: A14 -> 13
rule_38: A15 -> A16 A17
rule_39: A16 -> 16
rule_40: A17 -> 14 A18
rule_41: A17 -> 15 A19
rule_42: A18 -> 1
rule_43: A18 -> 2
rule_44: A18 -> 3
rule_45: A18 -> 4
rule_46: A18 -> 5
rule_47: A19 -> 1
rule_48: A19 -> 2
rule_49: A19 -> 3
rule_50: A19 -> 4
rule_51: A19 -> 5
rule_52: A20 -> A21 A22
rule_53: A21 -> 17
rule_54: A22 -> 14 A23
rule_55: A22 -> 15 A24
rule_56: A23 -> 1
rule_57: A23 -> 2
rule_58: A23 -> 3
rule_59: A23 -> 4
rule_60: A23 -> 5
rule_61: A24 -> 1
rule_62: A24 -> 2
rule_63: A24 -> 3
rule_64: A24 -> 4
rule_65: A24 -> 5
rule_66: A25 -> 18 A26
rule_67: A25 -> 19 A27
rule_68: A26 -> 1
rule_69: A26 -> 2
rule_70: A26 -> 3
rule_71: A26 -> 4
rule_72: A26 -> 5
rule_73: A27 -> 1
rule_74: A27 -> 2
rule_75: A27 -> 3
rule_76: A27 -> 4
rule_77: A27 -> 5
rule_78: A27 -> 20
rule_79: A28 -> 18 A29
rule_80: A28 -> 19 A30
rule_81: A29 -> 1
rule_82: A29 -> 2
rule_83: A29 -> 3
rule_84: A29 -> 4
rule_85: A29 -> 5
rule_86: A30 -> 1
rule_87: A30 -> 2
rule_88: A30 -> 3
rule_89: A30 -> 4
rule_90: A30 -> 5
rule_91: A31 -> A32
rule_92: A31 -> A33
rule_93: A31 -> A34
rule_94: A31 -> A35
rule_95: A31 -> A36
rule_96: A31 -> A37
rule_97: A31 -> A38
rule_98: A31 -> A39
rule_99: A31 -> A40
rule_100: A31 -> A41
rule_101: A31 -> A42
rule_102: A31 -> A43
rule_103: A32 -> 7
rule_104: A33 -> 7
rule_105: A34 -> 7
rule_106: A35 -> 7
rule_107: A36 -> 7
rule_108: A37 -> 7
rule_109: A38 -> 7
rule_110: A39 -> 7
rule_111: A40 -> 7
rule_112: A41 -> 7
rule_113: A42 -> 7
rule_114: A43 -> 7
rule_115: A44 -> 21 A45
rule_116: A45 -> 8
rule_117: A46 -> A47 A25
rule_118: A47 -> 22
rule_119: A48 -> A49 A44 A15 A31
rule_120: A49 -> 23 A20
rule_121: A50 -> A51 A28
rule_122: A51 -> 24
rule_123: A52 -> 25
rule_124: A52 -> A53 A3
rule_125: A53 -> 26
rule_126: A54 -> 27 A48
rule_127: A55 -> 28
rule_128: A56 -> A57
rule_129: A57 -> A58 A60 A10 A59
rule_130: A58 -> 29 A5
rule_131: A59 -> 30 A46
rule_132: A60 -> 32 A52 33
rule_133: A61 -> 35
rule_134: A62 -> 35
rule_135: A63 -> 35
rule_136: A64 -> A48
rule_137: A64 -> A52 34
rule_138: A65 -> A48 A63
rule_139: A65 -> A50 A61
rule_140: A65 -> A52 A62

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