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I don't think you can do what you did because starts some kind of circular logic thing, and it also clearly gets you to the wrong answer. Do what I said before, check why your method cannot be correct and then use my method, and see the difference in answers.
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"Great spirits have always encountered violent opposition from mediocre minds" -- Albert Einstein
"A clear indication of women's superiority over man is their refusal to play air guitar." --Frank Zappa
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