%!PS

% begin included library code
% see https://codeberg.org/Firedrake/postscript-libraries/
/test.end {
    ( ) print
    test.count 0 gt {
        (Passed ) print
        test.pass (...) cvs print
        (/) print
        test.count (...) cvs print
        ( \() print
        test.pass 100 mul test.count idiv (...) cvs print
        (%\)) print
        (\r\n) print
    } if
} bind def

/reverse {
    1 dict begin
    dup length /l exch def
    [ exch
      aload pop
      2 1 l {
          -1 roll
      } for
    ]
    end
} bind def

/listmax {
    { max } reduce
} bind def

/keys { % dict -> array of dict keys
    [ exch
      {
          pop
      } forall
    ]
} bind def

/quicksort.with_comparator { % [ a c b ] { comparator } -> [ a b c ]
    2 dict begin
    /cmp exch def
    /arr exch def
    arr length 0 gt {
        0 arr length 1 sub quicksort.main
    } if
    arr
    end
} bind def

/permute { % [array] {proc} permute runs proc on each permutation of array
    7 dict begin
    /permute.subproc exch def
    /permute.a exch def
    /permute.n permute.a length def
    /permute.c [ permute.n { 0 } repeat ] def
    permute.a permute.subproc
    /permute.i 0 def
    {
        permute.i permute.n ge {
            exit
        } if
        permute.c permute.i get permute.i lt {
            permute.i 2 mod 0 eq {
                0 permute.i permute.swap
            } {
                permute.c permute.i get permute.i permute.swap
            } ifelse
            permute.a permute.subproc
            permute.c permute.i get 1 add permute.c exch permute.i exch put
            /permute.i 0 def
        } {
            permute.c permute.i 0 put
            /permute.i permute.i 1 add def
        } ifelse
    } loop
    end
} bind def

/permute.swap {
    /permute.bi exch def
    /permute.ai exch def
    permute.a permute.ai get
    permute.a permute.bi get
    permute.a exch permute.ai exch put
    permute.a exch permute.bi exch put
} bind def

/quicksort.cmp {
    2 copy
    lt {
        pop pop -1
    } {
        gt {
            1
        } {
            0
        } ifelse
    } ifelse
} bind def

/quicksort {
    { quicksort.cmp } quicksort.with_comparator
} bind def

/quicksort.swap {
    2 dict begin
    /bi exch def
    /ai exch def
    arr ai get
    arr bi get
    arr exch ai exch put
    arr exch bi exch put
    end
} bind def

/toset { % array -> dict of (value, true)
    << exch
       {
           true
       } forall
    >>
} bind def

/quicksort.partition {
    3 dict begin
    /pivot arr hi lo add 2 idiv get def
    /i lo 1 sub def
    /j hi 1 add def
    {
        {
            /i i 1 add def
            arr i get pivot cmp 0 ge {
                exit
            } if
        } loop
        {
            /j j 1 sub def
            arr j get pivot cmp 0 le {
                exit
            } if
        } loop
        i j ge {
            j
            exit
        } if
        i j quicksort.swap
    } loop
    end
} bind def

/reduce { % array proc -> value
    2 dict begin
    /p exch def
    /a exch def
    a 0 get
    1 1 a length 1 sub {
        a exch get
        p
    } for
    end
} bind def

/test.start {
    print (:) print
    /test.pass 0 def
    /test.count 0 def
} bind def

/test {
    /test.count test.count 1 add def
    {
        /test.pass test.pass 1 add def
    } {
        ( ) print
        test.count (....) cvs print
        (-fail) print
    } ifelse
} bind def

/deepeq {
    2 dict begin
    /a exch def
    /b exch def
    a type b type eq {
        a type /dicttype eq {
            a length b length eq {
                <<
                    a {
                        pop
                        true
                    } forall
                    b {
                        pop
                        true
                    } forall
                >>
                true exch
                {
                    pop
                    dup a exch known {
                        dup b exch known {
                            dup a exch get exch b exch get deepeq not {
                                pop false
                            } if
                        } {
                            false
                        } ifelse
                    } {
                        false
                    } ifelse
                } forall
            } {
                false
            } ifelse
        } {
            a type dup /arraytype eq exch /stringtype eq or {
                a length b length eq {
                    true
                    0 1 a length 1 sub {
                        dup a exch get exch b exch get deepeq not {
                            pop false
                            exit
                        } if
                    } for
                } {
                    false
                } ifelse
            } {
                a b eq
            } ifelse
        } ifelse
    } {
        false
    } ifelse
    end
} bind def

/quicksort.main { % lo hi -> (null)
    3 dict begin
    /hi exch def
    /lo exch def
    /xit false def
    lo 0 lt {
        /xit true def
    } if
    hi 0 lt {
        /xit true def
    } if
    lo hi ge {
        /xit true def
    } if
    xit not {
        /p quicksort.partition def
        lo p quicksort.main
        p 1 add hi quicksort.main
    } if
    end
} bind def


% end included library code

/squareful {
    0 dict begin
    /lst exch def
    /squares 0 dict def
    /results [
        lst {
            /la exch def
            /squareful true def
            0 1 la length 2 sub {
                dup
                1 add la exch get
                exch
                la exch get
                add
                /cs exch def
                /mx squares length dup mul def
                {
                    cs mx le {
                        exit
                    } if
                    /mx squares length 1 add dup mul def
                    squares mx true put
                } loop
                squares cs known not {
                    /squareful false def
                    exit
                } if
            } for
            squareful {
                [ la aload pop ]
            } if
        } permute
    ] def
    /base lst listmax 1 add def
    [
        [
            results {
                { exch base mul add } reduce
            } forall
        ] toset keys quicksort {
            [ exch
              {
                  dup 0 eq {
                      pop exit
                  } if
                  dup base mod exch base idiv
              } loop
            ] reverse
        } forall
    ]
    end
} bind def

(squareful) test.start
[1 17 8] squareful [[1 8 17] [17 8 1]] deepeq test
[2 2 2] squareful [[2 2 2]] deepeq test
test.end