How to exit emacs with `q` when man inside emacs is opened

Default behavior of man <command> (opens inside less) when q is pressed it is closed.

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I am using following to open MANPAGER with emacs:

emacsclient -nw -e "(let ((Man-notify-method 'bully)) (man "$1"))"

Here pressing q closes buffer but does not close the emacs like Ctrl-x Ctrl-c does. Is it possible to bind q into the same action Ctrl-x Ctrl-c to exit the emacs and get back to shell.

(define-key Man-mode-map "q" 'save-buffers-kill-emacs)

emacsclient -nw -e "(let ((Man-notify-method 'bully)) (man "$1") (define-key Man-mode-map "q" 'save-buffers-kill-emacs))"