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# Angles
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rev_deg = 360
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compass_dir_headings = {'N': 0, 'E': 90, 'S': 180, 'W': 270}
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def compass2heading(compass):
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    heading = None
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    for dir_ in reversed(compass):
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        dir_heading = compass_dir_headings[dir_]
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        if heading == None: heading = dir_heading
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        else:
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            sum_ = dir_heading + heading
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            if abs(dir_heading - heading) > rev_deg/2: sum_ += rev_deg
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            heading = sum_/2. % rev_deg
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    return heading
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