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## 문제

A ternary numerical system (also called base 3) has three as its base. Just as a binary digit is called a bit in base 2, a ternary digit is surprisingly called a trit. The trits are 0, 1 and 2. For this problem, you will write an interpreter for a ternary machine that accepts as input a program consisting of a string of trits and executes it. Instructions for this machine consist of an opcode sometimes followed by a parameter. The opcodes for the machine follow. S1 and S2 refer to the item at the top of the stack and the 2nd item on the stack respectively. When these are used below, it implies they are removed from the stack for the given instruction (popped).

Opcode Parameter Description
000 Number Push positive Number onto stack
001 Number Push negative Number onto stack
020   Duplicate the top item on the stack
021   Swap the top two items on the stack
022   Discard the top item on the stack
1000   Add S1 + S2 and push result onto stack.
1001   Subtract S2S1 and push result onto stack.
1002   Multiply S1 x S2 and push result onto stack.
1010   Divide S2 ÷ S1 and push result onto stack.
1011   Compute module S2 % S1 and push result onto stack.
110   Store the Value S1 at the machine’s memory heap address specified by S2.
111   Push the Value from the machine’s memory heap address specified by S1 onto the stack.
200 Label Set a label mark at the point in the program after this instruction. This may the destination of a Jump or Call.
201 Label Call the subroutine at the specified label.
202 Label Jump to the specified label.
210 Label Jump to the label if S1 is 0.
211 Label Jump to the label S1 is negative.
212   End subroutine and transfer control back to the location where it was called from.
222   End the program and halt the machine.
1200   Output the character from S1.
1201   Output the decimal number from S1.
1210   Read a character from the input and place it in the machine’s memory heap at the address specified by S1.
1211   Read a decimal number from the input and place it in the machine’s memory heap at the address specified by S1.

The machine you will implement must support a stack of precisely 1024 items. Items can only be Values or characters. The memory heap is of arbitrary size, and possibly sparse. Addresses used to reference the heap are positive Values.

Number is a decimal integer from 1 to 31 bits in length. (Yes, it’s in bits not trits.) The end of the value is indicated by the trit 2. Ex. 100112 = 19 (decimal).

Value is a signed Number. Since Number is no more than 31 bits, a Value can be represented using a 32-bit quantity (-2147483647 ≤ Value ≤ 2147483647).

Label is a string of 1 to 128 trits of value 0 or 1. Its end is always indicated by a trit of value 2. If an attempt is made to redefine a Label mark, that is a RUN-TIME ERROR.

Subroutines calls may be nested (and recursive) to a maximum depth of 1024 (the top-level execution depth is 0).

Any illegal character (non-trit) encountered during execution should cause a RUN-TIME ERROR.

Program execution starts with the first character in the program and continues until the opcode 222 is reached or there is a RUN-TIME ERROR.

## 입력

Input consists of one or more lines. The first line contains a string of up to 8192 characters representing the program to execute (the terminating line feed is not part of the program to execute). If the program requires input (for opcodes 1210 and 1211), the input follows after the first line (after the line feed), on one or more lines as required by the program. If a program requires input, there will always be enough input supplied. Care should be taken when implementing the 1210 and 1211 opcodes so as to not consume too much input. Ex. For opcode 1211, only an optional leading minus sign and decimal digits should be read until a non-decimal digit is reached.

## 출력

The output consists of at least one line which is the output of the supplied ternary program and/or the message “RUN-TIME ERROR” if an error occurred during execution of the ternary program. Some possible RUN-TIME ERRORs include invalid character, invalid opcode, stack underflow, stack overflow, division by 0, undefined label, etc. If a RUN-TIME ERROR does occur, be sure to flush all pending output from the ternary program prior to printing RUN-TIME ERROR. Attempting to access an address in the machine’s heap that has not been previously set should retrieve a value of 0 – this is not a RUN-TIME error.

Note: It is possible that the ternary program will generate some output and then get a RUN-TIME ERROR. It is also possible that there are potential errors in the ternary program but these errors will not be reached during execution (ex. invalid character/opcode, missing label, redefined label, etc.). In this case, these RUN-TIME ERRORs will not be reported (which is correct).

## 예제 입력 1

000122000100001120201201000101021200000121000020000101121001210010001012202010000112200010001012022222


## 예제 출력 1

1
2
3
4
5
6
7
8
9
10


## 예제 입력 2

0001001000212000001101111212000001110111212000001000002120000011011012120000011000012120000011011102120000011110012120000011111121200000100000212000001021211000020001202012010001010212002001202000012021110100000012111021020120100010102120000010211100012100102000010202111021110220212200102222
12


## 예제 출력 2

How many? 1
1
2
3
5
8
13
21
34
55
89
144
233
377


The last line of input, “12”, is the input to the ternary program. In this case, the program requires a single number as input in response to the “How many?” question.

## 예제 입력 3

0001000001212002021112These are Illegal: RUN-TIME Error2001112000101021200222



## 예제 출력 3

ARUN-TIME ERROR


## 예제 입력 4

000100000121200202111220210022001112000101021200222This is NOT an error!!222



## 예제 출력 4

A