# lists

## List Processing Functions

This module contains functions for list processing.

Unless otherwise stated, all functions assume that position numbering starts at 1. That is, the first element of a list is at position 1.

Two terms `T1`

and `T2`

compare equal if
`T1 == T2`

evaluates to `true`

. They match
if `T1 =:= T2`

evaluates to `true`

.

Whenever an *ordering function*
`F`

is expected as argument, it is assumed that the
following properties hold of `F`

for all x, y and z:

if x

`F`

y and y`F`

x then x = y (`F`

is antisymmetric);if x

`F`

y and y`F`

z then x`F`

z (`F`

is transitive);x

`F`

y or y`F`

x (`F`

is total).

An example of a typical ordering function is less than or equal
to, `=</2`

.

#### Functions

### all(Pred, List) -> boolean()

`Pred = fun((Elem :: T) -> boolean())`

`List = [T]`

`T = term()`

Returns `true`

if

returns
`true`

for all elements

in

,
otherwise `false`

.

### any(Pred, List) -> boolean()

`Pred = fun((Elem :: T) -> boolean())`

`List = [T]`

`T = term()`

Returns `true`

if

returns
`true`

for at least one element

in

.

### append(ListOfLists) -> List1

`ListOfLists = [List]`

`List = List1 = [T]`

`T = term()`

Returns a list in which all the sub-lists of

have been appended. For example:

`> ``lists:append([[1, 2, 3], [a, b], [4, 5, 6]]).`

[1,2,3,a,b,4,5,6]

### append(List1, List2) -> List3

`List1 = List2 = List3 = [T]`

`T = term()`

Returns a new list

which is made from
the elements of

followed by the elements of

. For example:

`> ``lists:append("abc", "def").`

"abcdef"

`lists:append(A, B)`

is equivalent to `A ++ B`

.

### concat(Things) -> string()

`Things = [Thing]`

`Thing = atom() | integer() | float() | string()`

Concatenates the text representation of the elements
of

. The elements of

can be atoms,
integers, floats or strings.

`> ``lists:concat([doc, '/', file, '.', 3]).`

"doc/file.3"

### delete(Elem, List1) -> List2

`Elem = T`

`List1 = List2 = [T]`

`T = term()`

Returns a copy of

where the first element
matching

is deleted, if there is such an
element.

### dropwhile(Pred, List1) -> List2

`Pred = fun((Elem :: T) -> boolean())`

`List1 = List2 = [T]`

`T = term()`

Drops elements

from

while

returns `true`

and returns
the remaining list.

### duplicate(N, Elem) -> List

`N = integer() >= 0`

`Elem = T`

`List = [T]`

`T = term()`

Returns a list which contains

copies of the term

. For example:

`> ``lists:duplicate(5, xx).`

[xx,xx,xx,xx,xx]

### filter(Pred, List1) -> List2

`Pred = fun((Elem :: T) -> boolean())`

`List1 = List2 = [T]`

`T = term()`

is a list of all elements

in

for which

returns
`true`

.

### flatlength(DeepList) -> integer() >= 0

`DeepList = [term() | DeepList]`

Equivalent to `length(flatten(`

, but more
efficient.

### flatmap(Fun, List1) -> List2

`Fun = fun((A) -> [B])`

`List1 = [A]`

`List2 = [B]`

`A = B = term()`

Takes a function from

s to lists of

s, and a
list of

s (

) and produces a list of

s by applying the function to every element in

and appending the resulting lists.

That is, `flatmap`

behaves as if it had been defined as
follows:

flatmap(Fun, List1) -> append(map(Fun, List1)).

Example:

`> ``lists:flatmap(fun(X)->[X,X] end, [a,b,c]).`

[a,a,b,b,c,c]

### flatten(DeepList) -> List

`DeepList = [term() | DeepList]`

`List = [term()]`

Returns a flattened version of

.

### flatten(DeepList, Tail) -> List

`DeepList = [term() | DeepList]`

`Tail = List = [term()]`

Returns a flattened version of

with the tail

appended.

### foldl(Fun, Acc0, List) -> Acc1

`Fun = fun((Elem :: T, AccIn) -> AccOut)`

`Acc0 = Acc1 = AccIn = AccOut = term()`

`List = [T]`

`T = term()`

Calls

on successive elements `A`

of

, starting with

.

must return a new accumulator which is passed to
the next call. The function returns the final value of
the accumulator.

is returned if the list is empty.
For example:

>`lists:foldl(fun(X, Sum) -> X + Sum end, 0, [1,2,3,4,5]).`

15 >`lists:foldl(fun(X, Prod) -> X * Prod end, 1, [1,2,3,4,5]).`

120

### foldr(Fun, Acc0, List) -> Acc1

`Fun = fun((Elem :: T, AccIn) -> AccOut)`

`Acc0 = Acc1 = AccIn = AccOut = term()`

`List = [T]`

`T = term()`

Like `foldl/3`

, but the list is traversed from right to
left. For example:

>`P = fun(A, AccIn) -> io:format("~p ", [A]), AccIn end.`

#Fun<erl_eval.12.2225172> >`lists:foldl(P, void, [1,2,3]).`

1 2 3 void >`lists:foldr(P, void, [1,2,3]).`

3 2 1 void

`foldl/3`

is tail recursive and would usually be
preferred to `foldr/3`

.

### foreach(Fun, List) -> ok

`Fun = fun((Elem :: T) -> term())`

`List = [T]`

`T = term()`

Calls

for each element

in

. This function is used for its side effects and
the evaluation order is defined to be the same as the order
of the elements in the list.

### keydelete(Key, N, TupleList1) -> TupleList2

`Key = term()`

`N = integer() >= 1`

`TupleList1 = TupleList2 = [Tuple]`

`Tuple = tuple()`

Returns a copy of

where the first
occurrence of a tuple whose

th element compares equal to

is deleted, if there is such a tuple.

### keyfind(Key, N, TupleList) -> Tuple | false

`Key = term()`

`N = 1..tuple_size(Tuple)`

`TupleList = [Tuple]`

`Tuple = tuple()`

Searches the list of tuples `TupleList`

for a
tuple whose `N`

th element compares equal to `Key`

.
Returns `Tuple`

if such a tuple is found,
otherwise `false`

.

### keymap(Fun, N, TupleList1) -> TupleList2

`Fun = fun((Term1 :: term()) -> Term2 :: term())`

`N = integer() >= 1`

`TupleList1 = TupleList2 = [Tuple]`

`Tuple = tuple()`

Returns a list of tuples where, for each tuple in

, the

th element

of the tuple
has been replaced with the result of calling

.

Examples:

>`Fun = fun(Atom) -> atom_to_list(Atom) end.`

#Fun<erl_eval.6.10732646> 2>`lists:keymap(Fun, 2, [{name,jane,22},{name,lizzie,20},{name,lydia,15}]).`

[{name,"jane",22},{name,"lizzie",20},{name,"lydia",15}]

### keymember(Key, N, TupleList) -> boolean()

`Key = term()`

`N = 1..tuple_size(Tuple)`

`TupleList = [Tuple]`

`Tuple = tuple()`

Returns `true`

if there is a tuple in `TupleList`

whose `N`

th element compares equal to `Key`

, otherwise
`false`

.

### keymerge(N, TupleList1, TupleList2) -> TupleList3

`N = integer() >= 1`

`TupleList1 = [T1]`

`TupleList2 = [T2]`

`TupleList3 = [(T1 | T2)]`

`T1 = T2 = Tuple`

`Tuple = tuple()`

Returns the sorted list formed by merging

and

. The merge is performed on
the

th element of each tuple. Both

and

must be key-sorted prior to evaluating this
function. When two tuples compare equal, the tuple from

is picked before the tuple from

.

### keyreplace(Key, N, TupleList1, NewTuple) -> TupleList2

`Key = term()`

`N = integer() >= 1`

`TupleList1 = TupleList2 = [Tuple]`

`NewTuple = Tuple`

`Tuple = tuple()`

Returns a copy of

where the first
occurrence of a `T`

tuple whose

th element
compares equal to

is replaced with

, if there is such a tuple `T`

.

### keysearch(Key, N, TupleList) -> {value, Tuple} | false

`Key = term()`

`N = 1..tuple_size(Tuple)`

`TupleList = [Tuple]`

`Tuple = tuple()`

Searches the list of tuples `TupleList`

for a
tuple whose `N`

th element compares equal to `Key`

.
Returns `{value, Tuple}`

if such a tuple is found,
otherwise `false`

.

## Note!

This function is retained for backward compatibility.
The function `lists:keyfind/3`

(introduced in R13A)
is in most cases more convenient.

### keysort(N, TupleList1) -> TupleList2

`N = integer() >= 1`

`TupleList1 = TupleList2 = [Tuple]`

`Tuple = tuple()`

Returns a list containing the sorted elements of the list

. Sorting is performed on the

th
element of the tuples. The sort is stable.

### keystore(Key, N, TupleList1, NewTuple) -> TupleList2

`Key = term()`

`N = integer() >= 1`

`TupleList1 = [Tuple]`

`TupleList2 = [Tuple, ...]`

`NewTuple = Tuple`

`Tuple = tuple()`

Returns a copy of

where the first
occurrence of a tuple `T`

whose

th element
compares equal to

is replaced with

, if there is such a tuple `T`

. If there
is no such tuple `T`

a copy of

where
[

] has been appended to the end is
returned.

### keytake(Key, N, TupleList1) -> {value, Tuple, TupleList2} | false

`Key = term()`

`N = integer() >= 1`

`TupleList1 = TupleList2 = [tuple()]`

`Tuple = tuple()`

Searches the list of tuples

for a tuple
whose

th element compares equal to

.
Returns `{value, `

if such a tuple is
found, otherwise `false`

.

is a copy
of

where the first occurrence of

has been removed.

### last(List) -> Last

`List = [T, ...]`

`Last = T`

`T = term()`

Returns the last element in

.

### map(Fun, List1) -> List2

`Fun = fun((A) -> B)`

`List1 = [A]`

`List2 = [B]`

`A = B = term()`

Takes a function from

s to

s, and a list of

s and produces a list of

s by applying
the function to every element in the list. This function is
used to obtain the return values. The evaluation order is
implementation dependent.

### mapfoldl(Fun, Acc0, List1) -> {List2, Acc1}

`Fun = fun((A, AccIn) -> {B, AccOut})`

`Acc0 = Acc1 = AccIn = AccOut = term()`

`List1 = [A]`

`List2 = [B]`

`A = B = term()`

`mapfoldl`

combines the operations of `map/2`

and
`foldl/3`

into one pass. An example, summing
the elements in a list and double them at the same time:

>`lists:mapfoldl(fun(X, Sum) -> {2*X, X+Sum} end,`

`0, [1,2,3,4,5]).`

{[2,4,6,8,10],15}

### mapfoldr(Fun, Acc0, List1) -> {List2, Acc1}

`Fun = fun((A, AccIn) -> {B, AccOut})`

`Acc0 = Acc1 = AccIn = AccOut = term()`

`List1 = [A]`

`List2 = [B]`

`A = B = term()`

`mapfoldr`

combines the operations of `map/2`

and
`foldr/3`

into one pass.

### max(List) -> Max

`List = [T, ...]`

`Max = T`

`T = term()`

Returns the first element of

that compares
greater than or equal to all other elements of

.

### member(Elem, List) -> boolean()

`Elem = term()`

`List = [term()]`

Returns `true`

if `Elem`

matches some element of
`List`

, otherwise `false`

.

### merge(ListOfLists) -> List1

`ListOfLists = [List]`

`List = List1 = [T]`

`T = term()`

Returns the sorted list formed by merging all the sub-lists
of

. All sub-lists must be sorted prior to
evaluating this function. When two elements compare equal,
the element from the sub-list with the lowest position in

is picked before the other element.

### merge(List1, List2) -> List3

`List1 = [X]`

`List2 = [Y]`

`List3 = [(X | Y)]`

`X = Y = term()`

Returns the sorted list formed by merging

and

. Both

and

must be
sorted prior to evaluating this function. When two elements
compare equal, the element from

is picked
before the element from

.

### merge(Fun, List1, List2) -> List3

`Fun = fun((A, B) -> boolean())`

`List1 = [A]`

`List2 = [B]`

`List3 = [(A | B)]`

`A = B = term()`

Returns the sorted list formed by merging

and

. Both

and

must be
sorted according to the ordering function

prior to evaluating this function.

should return `true`

if

compares less
than or equal to

in the ordering, `false`

otherwise. When two elements compare equal, the element from

is picked before the element from

.

### merge3(List1, List2, List3) -> List4

`List1 = [X]`

`List2 = [Y]`

`List3 = [Z]`

`List4 = [(X | Y | Z)]`

`X = Y = Z = term()`

Returns the sorted list formed by merging

,

and

. All of

,

and

must be sorted prior to
evaluating this function. When two elements compare equal,
the element from

, if there is such an element,
is picked before the other element, otherwise the element
from

is picked before the element from

.

### min(List) -> Min

`List = [T, ...]`

`Min = T`

`T = term()`

Returns the first element of

that compares
less than or equal to all other elements of

.

### nth(N, List) -> Elem

`N = integer() >= 1`

`List = [T, ...]`

`Elem = T`

`T = term()`

Returns the

th element of

. For example:

`> ``lists:nth(3, [a, b, c, d, e]).`

c

### nthtail(N, List) -> Tail

`N = integer() >= 0`

`List = [T, ...]`

`Tail = [T]`

`T = term()`

Returns the

th tail of

, that is, the sublist of

starting at

and continuing up to
the end of the list. For example:

>`lists:nthtail(3, [a, b, c, d, e]).`

[d,e] >`tl(tl(tl([a, b, c, d, e]))).`

[d,e] >`lists:nthtail(0, [a, b, c, d, e]).`

[a,b,c,d,e] >`lists:nthtail(5, [a, b, c, d, e]).`

[]

### partition(Pred, List) -> {Satisfying, NotSatisfying}

`Pred = fun((Elem :: T) -> boolean())`

`List = Satisfying = NotSatisfying = [T]`

`T = term()`

Partitions

into two lists, where the first list
contains all elements for which

returns
`true`

, and the second list contains all elements for
which

returns `false`

.

Examples:

>`lists:partition(fun(A) -> A rem 2 == 1 end, [1,2,3,4,5,6,7]).`

{[1,3,5,7],[2,4,6]} >`lists:partition(fun(A) -> is_atom(A) end, [a,b,1,c,d,2,3,4,e]).`

{[a,b,c,d,e],[1,2,3,4]}

See also `splitwith/2`

for a different way to partition
a list.

### prefix(List1, List2) -> boolean()

`List1 = List2 = [T]`

`T = term()`

Returns `true`

if

is a prefix of

, otherwise `false`

.

### reverse(List1) -> List2

`List1 = List2 = [T]`

`T = term()`

Returns a list with the elements in

in reverse order.

### reverse(List1, Tail) -> List2

`List1 = Tail = List2 = [term()]`

Returns a list with the elements in `List1`

in reverse order, with the tail `Tail`

appended. For
example:

`> ``lists:reverse([1, 2, 3, 4], [a, b, c]).`

[4,3,2,1,a,b,c]

### seq(From, To) -> Seq

`From = To = integer()`

`Seq = [integer()]`

### seq(From, To, Incr) -> Seq

`From = To = Incr = integer()`

`Seq = [integer()]`

Returns a sequence of integers which starts with

and contains the successive results of adding

to
the previous element, until

has been reached or
passed (in the latter case,

is not an element of
the sequence).

defaults to 1.

Failure: If

and

is positive, or if

and

is
negative, or if

and

.

The following equalities hold for all sequences:

length(lists:seq(From, To)) == To-From+1 length(lists:seq(From, To, Incr)) == (To-From+Incr) div Incr

Examples:

>`lists:seq(1, 10).`

[1,2,3,4,5,6,7,8,9,10] >`lists:seq(1, 20, 3).`

[1,4,7,10,13,16,19] >`lists:seq(1, 0, 1).`

[] >`lists:seq(10, 6, 4).`

[] >`lists:seq(1, 1, 0).`

[1]

### sort(List1) -> List2

`List1 = List2 = [T]`

`T = term()`

Returns a list containing the sorted elements of

.

### sort(Fun, List1) -> List2

`Fun = fun((A :: T, B :: T) -> boolean())`

`List1 = List2 = [T]`

`T = term()`

Returns a list containing the sorted elements of

, according to the ordering function

.

should return `true`

if

compares less than or equal to

in the
ordering, `false`

otherwise.

### split(N, List1) -> {List2, List3}

`N = integer() >= 0`

`List1 = List2 = List3 = [T]`

`T = term()`

Splits

into

and

.

contains the first

elements and

the rest of the elements (the

th tail).

### splitwith(Pred, List) -> {List1, List2}

`Pred = fun((T) -> boolean())`

`List = List1 = List2 = [T]`

`T = term()`

Partitions

into two lists according to

. `splitwith/2`

behaves as if it is defined
as follows:

splitwith(Pred, List) -> {takewhile(Pred, List), dropwhile(Pred, List)}.

Examples:

>`lists:splitwith(fun(A) -> A rem 2 == 1 end, [1,2,3,4,5,6,7]).`

{[1],[2,3,4,5,6,7]} >`lists:splitwith(fun(A) -> is_atom(A) end, [a,b,1,c,d,2,3,4,e]).`

{[a,b],[1,c,d,2,3,4,e]}

See also `partition/2`

for a different way to partition
a list.

### sublist(List1, Len) -> List2

`List1 = List2 = [T]`

`Len = integer() >= 0`

`T = term()`

Returns the sub-list of

starting at position 1
and with (max)

elements. It is not an error for

to exceed the length of the list, in that case
the whole list is returned.

### sublist(List1, Start, Len) -> List2

`List1 = List2 = [T]`

`Start = integer() >= 1`

`Len = integer() >= 0`

`T = term()`

Returns the sub-list of

starting at

and with (max)

elements. It is not an error for

to exceed the length of the list.

>`lists:sublist([1,2,3,4], 2, 2).`

[2,3] >`lists:sublist([1,2,3,4], 2, 5).`

[2,3,4] >`lists:sublist([1,2,3,4], 5, 2).`

[]

### subtract(List1, List2) -> List3

`List1 = List2 = List3 = [T]`

`T = term()`

Returns a new list

which is a copy of

, subjected to the following procedure: for each
element in

, its first occurrence in

is deleted. For example:

`> ``lists:subtract("123212", "212").`

"312".

`lists:subtract(A, B)`

is equivalent to `A -- B`

.

## Warning!

The complexity of `lists:subtract(A, B)`

is proportional
to `length(A)*length(B)`

, meaning that it will be very slow if
both `A`

and `B`

are long lists.
(Using ordered lists and
ordsets:subtract/2
is a much better choice if both lists are long.)

### suffix(List1, List2) -> boolean()

`List1 = List2 = [T]`

`T = term()`

Returns `true`

if

is a suffix of

, otherwise `false`

.

### sum(List) -> number()

`List = [number()]`

Returns the sum of the elements in

.

### takewhile(Pred, List1) -> List2

`Pred = fun((Elem :: T) -> boolean())`

`List1 = List2 = [T]`

`T = term()`

Takes elements

from

while

returns `true`

, that is,
the function returns the longest prefix of the list for which
all elements satisfy the predicate.

### ukeymerge(N, TupleList1, TupleList2) -> TupleList3

`N = integer() >= 1`

`TupleList1 = [T1]`

`TupleList2 = [T2]`

`TupleList3 = [(T1 | T2)]`

`T1 = T2 = Tuple`

`Tuple = tuple()`

Returns the sorted list formed by merging

and

. The merge is performed on the

th element of each tuple. Both

and

must be key-sorted without duplicates
prior to evaluating this function. When two tuples compare
equal, the tuple from

is picked and the
one from

deleted.

### ukeysort(N, TupleList1) -> TupleList2

`N = integer() >= 1`

`TupleList1 = TupleList2 = [Tuple]`

`Tuple = tuple()`

Returns a list containing the sorted elements of the list

where all but the first tuple of the
tuples comparing equal have been deleted. Sorting is
performed on the

th element of the tuples.

### umerge(ListOfLists) -> List1

`ListOfLists = [List]`

`List = List1 = [T]`

`T = term()`

Returns the sorted list formed by merging all the sub-lists
of

. All sub-lists must be sorted and
contain no duplicates prior to evaluating this function.
When two elements compare equal, the element from the
sub-list with the lowest position in

is
picked and the other one deleted.

### umerge(List1, List2) -> List3

`List1 = [X]`

`List2 = [Y]`

`List3 = [(X | Y)]`

`X = Y = term()`

Returns the sorted list formed by merging

and

. Both

and

must be
sorted and contain no duplicates prior to evaluating this
function. When two elements compare equal, the element from

is picked and the one from

deleted.

### umerge(Fun, List1, List2) -> List3

`Fun = fun((A, B) -> boolean())`

`List1 = [A]`

`List2 = [B]`

`List3 = [(A | B)]`

`A = B = term()`

Returns the sorted list formed by merging

and

. Both

and

must be
sorted according to the ordering function
`Fun`

and contain no duplicates prior to evaluating
this function.

should return `true`

if

compares less than or equal to

in the
ordering, `false`

otherwise. When two elements compare
equal, the element from

is picked and the one from

deleted.

### umerge3(List1, List2, List3) -> List4

`List1 = [X]`

`List2 = [Y]`

`List3 = [Z]`

`List4 = [(X | Y | Z)]`

`X = Y = Z = term()`

Returns the sorted list formed by merging

,

and

. All of

,

and

must be sorted and contain no
duplicates prior to evaluating this function. When two
elements compare equal, the element from

is
picked if there is such an element, otherwise the element
from

is picked, and the other one deleted.

### unzip(List1) -> {List2, List3}

`List1 = [{A, B}]`

`List2 = [A]`

`List3 = [B]`

`A = B = term()`

"Unzips" a list of two-tuples into two lists, where the first list contains the first element of each tuple, and the second list contains the second element of each tuple.

### unzip3(List1) -> {List2, List3, List4}

`List1 = [{A, B, C}]`

`List2 = [A]`

`List3 = [B]`

`List4 = [C]`

`A = B = C = term()`

"Unzips" a list of three-tuples into three lists, where the first list contains the first element of each tuple, the second list contains the second element of each tuple, and the third list contains the third element of each tuple.

### usort(List1) -> List2

`List1 = List2 = [T]`

`T = term()`

Returns a list containing the sorted elements of

where all but the first element of the elements
comparing equal have been deleted.

### usort(Fun, List1) -> List2

`Fun = fun((T, T) -> boolean())`

`List1 = List2 = [T]`

`T = term()`

Returns a list which contains the sorted elements of

where all but the first element of the elements
comparing equal according to the ordering function

have been deleted.

should return
`true`

if `A`

compares less than or equal to
`B`

in the ordering, `false`

otherwise.

### zip(List1, List2) -> List3

`List1 = [A]`

`List2 = [B]`

`List3 = [{A, B}]`

`A = B = term()`

"Zips" two lists of equal length into one list of two-tuples, where the first element of each tuple is taken from the first list and the second element is taken from corresponding element in the second list.

### zip3(List1, List2, List3) -> List4

`List1 = [A]`

`List2 = [B]`

`List3 = [C]`

`List4 = [{A, B, C}]`

`A = B = C = term()`

"Zips" three lists of equal length into one list of three-tuples, where the first element of each tuple is taken from the first list, the second element is taken from corresponding element in the second list, and the third element is taken from the corresponding element in the third list.

### zipwith(Combine, List1, List2) -> List3

`Combine = fun((X, Y) -> T)`

`List1 = [X]`

`List2 = [Y]`

`List3 = [T]`

`X = Y = T = term()`

Combine the elements of two lists of equal length into one
list. For each pair

of list elements from the two
lists, the element in the result list will be

.

`zipwith(fun(X, Y) -> {X,Y} end, List1, List2)`

is
equivalent to `zip(List1, List2)`

.

Example:

`> ``lists:zipwith(fun(X, Y) -> X+Y end, [1,2,3], [4,5,6]).`

[5,7,9]

### zipwith3(Combine, List1, List2, List3) -> List4

`Combine = fun((X, Y, Z) -> T)`

`List1 = [X]`

`List2 = [Y]`

`List3 = [Z]`

`List4 = [T]`

`X = Y = Z = T = term()`

Combine the elements of three lists of equal length into one
list. For each triple

of list elements from
the three lists, the element in the result list will be

.

`zipwith3(fun(X, Y, Z) -> {X,Y,Z} end, List1, List2, List3)`

is equivalent to `zip3(List1, List2, List3)`

.

Examples:

>`lists:zipwith3(fun(X, Y, Z) -> X+Y+Z end, [1,2,3], [4,5,6], [7,8,9]).`

[12,15,18] >`lists:zipwith3(fun(X, Y, Z) -> [X,Y,Z] end, [a,b,c], [x,y,z], [1,2,3]).`

[[a,x,1],[b,y,2],[c,z,3]]