is_increasing () {
    # Tests if the arguments are monotonally increasing. Returns 1 if
    # monotone increasing; 0 if not.
    local output=1
    local difference=0
    local prev=""

    for entry in $@; do

        # Skip the first value since there is nothing to compare against.
        if [ -z $prev ]; then
            prev=$entry;
            continue;
        fi

        # If an entry is less than or equal to the previous entry, the arguments
        # are not monotonally increasing.
        if [ $entry -le $prev ]; then
            output=0
            break
        fi

        prev=$entry

    done

    echo $output

}

is_monotone () {
    # Uses is_increasing to check if the arguments are monotonally
    # increasing OR decreasing. Returns 1 if the args are monotone,
    # 0 if not.

    # Look at the first two entries to see if we should test for
    # increasing or decreasing.
    if [ $2 -gt $1 ]; then
        echo $(is_increasing $@)
    elif [ $1 -gt $2 ]; then

        # To test for decreasing, simply check if they increase backwards.
        # Replace spaces with line breaks, cat the column in reverse order, 
        # then use xargs to parse back into a list of args.
        echo $(is_increasing $(echo $@ | tr ' ' '\n' | tac | xargs))
    else

        # If the first two entries are equal, then the arguments are not monotone.
        echo 0
    fi
}

is_gradual () {
    # Checks to see if a series of arguments change gradually. If the
    # absolute differences between each entry are 3 or smaller, return 1.
    # Otherwise, returns 0

    local output=1
    local prev=""

    for entry in $@; do

        # Skip the first value since there is nothing to compare against.
        if [ -z $prev ]; then
            prev=$entry;
            continue;
        fi

        difference=$((entry - prev))

        if [ $difference -ge 4 ] || [ $difference -le -4 ]; then
            output=0
            break
        fi

        prev=$entry

    done

    echo $output

}

is_gradual_monotone () {
    # Echoes 1 if the arguments are a gradual monotone series; 0 if not.

    if [ $(is_monotone $@) -eq 1 ] && [ $(is_gradual $@) -eq 1 ]; then
        echo 1
    else
        echo 0
    fi

}

main_2_1 () {
    num_gradual_monotone=0

    while read line; do
        line_is_gradual_monotone=$(is_gradual_monotone $line)
        num_gradual_monotone=$((num_gradual_monotone + line_is_gradual_monotone))
    done <<< $(cat input.txt)

    echo $num_gradual_monotone
}

# main_2_1