A dictionary is a set of key-value pairs, for example:

{'color':'red', 'price':2, 7:'test', 100:-100}

As you can see,keys and values can be strings or integers. What’s more, values can also be dictionaries or variable references. Here is the formal definition ofterms that will be used soon:

key::=INTEGER | STRING

value::=INTEGER | STRING | dict

pair::=key ':' value

dict::='{' [pair (',' pair)*] '}'

var::='a'|'b'|'c'|...|'z'

slot::=var('[' key ']')*

lvar::=slot

rvar::=slot | value

Here('[' key ']')*means zero or more subsc ripts, [pair (',' pair)*]means zero or more key-value pairs.

Strings are always enclosed by single quotes ('') and consists of up to 10 lower-case letters. Integers always have absolute values of no more than 1000. You can insert spaces anywhere, except inside strings or integers. For example,{ 'a':-1}and{'a' : -1}are the same, but{'a b':1}and{'a':- 1}are both illegal.

Your task is to execute a series of commands and printtheresults. There are 3 kinds of commands:

1.Assignment: =

Afterassigning a slot to a slot(rather than a value), the left-hand slotwill be holdinga reference to the right-hand. For example, After executing the following commands,b[1][0]is 1, rather than 0:

a = {0:0}

b = {}

b[1] = a

a[0] = 1

Slots must be assigned before it isreadorsubsc ripted , and integers and strings cannot be subsc ripted. Consider the following comammd list:

c = {}

c[0] = 3

c[1] = c[0]

d[0] = 'i'

c = d

d = c[1]['a']

c[2][2] = 2

The first three commands are legal, but the nexttwoarebothillegal because slotdmust be assigned before it is read or subsc ripted. The last three arealsoillegal.

2.Length:length()

Output the number of key-value pairs in the slot. Note that nested pairs are not counted. For example:

a = {0: {0:0, 1:1}}

length(a)

will output 1, not 3. In this command, it is guaranteed thatis storing a dictionary, not a string or an integer.

3.Infinity test:test()

If the slot can be subsc ripted indefinitely, output 1. Otherwise, output 0. For example, after executing the following command list:

d = {}

d[0] = d

Thendis infinite, sinced[0][0][0][0][0][0]... is alwaysd. In this command, it is guaranteed thatis storing a dictionary, not a string or an integer.

The term definitions in this problem use a modified BNF grammar notation that is described in the official documentation of the Python programming language. Here is the explanation of the notation, extracted from the documentation:

Each rule begins with a name (which is the name defined by the rule) and ::=. A vertical bar (|) is used to separate alternatives; it is the least binding operator in this notation. A star (*) means zero or more repetitions of the preceding item; likewise, a plus (+) means one or more repetitions, and a phrase enclosed in square brackets ([ ]) means zero or one occurrences (in other words, the enclosed phrase is optional). The * and + operators bind as tightly as possible; parentheses are used for grouping. Literal strings are enclosed in quotes. White space is only meaningful to separate tokens. Rules are normally contained on a single line; rules with many alternatives may be formatted alternatively with each line after the first beginning with a vertical bar

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