[colug-432] Exit Status of First Program in Bourne Shell Pipeline

[jep200404 at columbus.rr.com]

How would you improve the following script?

    #!/bin/sh
    
    # This script executes the arguments as a command,
    # then outputs whether or not command output anything and
    # whether or not command failed (crashed).
    #
    # Two lines are output:
    # First line:
    #     1 means command output something
    #     0 means command did not change anything
    # Second line:
    #     1 means command failed (non-zero exit status)
    #     0 means command exitted normally
    
    pipe=~/command_to_wc.pipe
    rm -f "${pipe}"
    mknod "${pipe}" p
    "$@" >"${pipe}" 2>/dev/null &
    pid="$!"
    n=`wc -c <"${pipe}"`
    if [ "$n" = '0' ]; then
        echo 0 ;# command did not output anything
    else
        echo 1 ;# command output something
    fi
    if wait $pid; then
        echo 0 ;# normal
    else
        echo 1 ;# failure
    fi
    rm -f "${pipe}"

I started with

    n=`"$@" | wc -c`

but I could not get the exit status of the "$@" command,
so I split the pipeline into to two chunks using the named pipe
to communicate between them. Can I get rid of the named pipe?

Need to:
    run in plain old boring (but oh so portable) Bourne shell
    so avoid nifty bash features such as but not limited to
        PIPESTATUS
        pipefail