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Sure, " @-"  it is not a comlplete move. Like "L c3-" is not a complete move. That is the entire idea of moving by mouse clicks: you first get a partial move in the the movefield, and then you click on the destination square to complete it, and the script sends it to the server. By chosing twice from about 10 possibilities, you effectively make a one-in-a-hundred choice, without ever having to be presented all 100 alternatives at once. The problem is that there is no mouse click that puts " @-" in the movefield, unlike the "L c3-", which you get by clicking a Lion on c3. But the server could put it there when it knows that you will need it there, when it knows that you must enter a suicide as continuemove.

I am not sure what you mean by 'auto-complete', also because the Play function that I have been using doesn't seem to have it. But if you mean  the drop-down menu of moves that appear when one clicks the movefield in Move mode... there doesn't seem to be anything 'auto' on that. It requires a click to open the menu, and then you have to read all the moves, match them to squares on the board mentally, and pick the move you need. 'Auto-complete' usually means that when you enter a partial move that can only be completed in a single way, the interface does that for you, without you having to do anything at all. This is what I do in the Sandbox test preset with the swap moves I gave to the Knights; when they make a friendly capture, the victim automatically appears on their square of origin, because the necessary freedrop needed to do that is the only continuation that could make the move legal. A pull-down menu presenting moves in text form is so much worse than just clicking the desired highlighted square that I would never consider using it. Having a button that forces " @-" in the movefield, similar to the Pass button, would be a better option; suicide side effects could then be entered (as continuemove) by feeding them to setlegal as moves of the just-moved piece to the victims, so that you could switch on the highlights by clicking that piece, overwrite the origin part of the move that appeared by this in the move field by pressing that Suicide button, and finally clicking the desired destination square to complete the move and send it.

The problem is that a similar solution is not available for freedrops, as this would require the piece type to be dropped to appear in the movefield, and we cannot have buttons for every participating piece type. This is why it needs guidance from the GAME code. One solution would be an (optional) argument of continuemove, for placement in the movefield as partial move, switching on the highlights of the highlights on the possible destination squares of a freedrop or suicide. An alternative would be to make setlegal accept a piece label or @ as origin, to indicate legal freedrops or suicides. This could be used by the JavaScript to trigger placing it as origin in the movefield, switching on the highlights for it. Or you could have a button for it, which on pressing would put " @-" in the move field, and switch on the highlights on the destinations on all moves with @ as origin. There could also be a Drop button, which would similarly enable all moves in legalMoves that have a piece label as origin (hoping that they all use the same piece label, or that their destination uniquely determines what the piece type should be).

A more elaborate alternative is to have the legalMoves array not just describe the upcoming leg of complex moves, but the entire move, as arrays of 2, 4, 6, ... squares. There wouldn't even be need for communication with the server through continuemove then; the JavaScript would handle it all up to the point where the move is known to be complete, and only then send it to the server. (You could still make an exception for promotion, which would need another screen anyway.) E.g. in a CV with a non-standard castling, where the Rook can be freely placed independent of the King (assumed to start on f1 on a 10-wide board in the example), you could have something like:

legalMoves = [["f1","e1"], ["f1","g1"],["f1","h1","j1","g1"],["h1","h1","j1","f1"],["f1","i1","j1","h1"],["f1","i1","j1","g1"],["f1","i1","j1","f1"], ...];

After clicking the King (e1, g1, h1 and i1 get highlighted), and the empty square i1, the JavaScript would see that this second square only occurs in longer moves, that all have "j1" as next square. It would therefore automatically select the Rook on j1, and highlight the possibilities for the following square, h1, g1 and f1. A click on one of those would finish the move, and cause it to be uploaded (e.g. as K f1-i1; R j1-f1). With 3 clicks you would have specified the move. If there is ambiguity w.r.t. the number of legs (e.g. K f1-g1 could be a normal move or a castling) the JavaScript could err on the safe side and refrain from automatic sending; the user could press Move to force sending, or continue clicking the Rook for castling. There would be no auto-selection of the Rook, because j1 would not be the 3rd square in all the moves that matchetd f1-g1 for the first two, as some of the moves did not have a 3rd square. Instead of square names the array could of course also contain piece labels or @, to indicate the corresponding leg of the move is a freedrop or suicide.