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This puzzle is borrowed from   [http://math-frolic.blogspot.co.uk/2012/08/mind-wrenching.html math-frolic.blogspot].


Given the following twelve statements, which of them are true?
<pre>
 1.  This is a numbered list of twelve statements.
 2.  Exactly 3 of the last 6 statements are true.
 3.  Exactly 2 of the even-numbered statements are true.
 4.  If statement 5 is true, then statements 6 and 7 are both true.
 5.  The 3 preceding statements are all false.
 6.  Exactly 4 of the odd-numbered statements are true.
 7.  Either statement 2 or 3 is true, but not both.
 8.  If statement 7 is true, then 5 and 6 are both true.
 9.  Exactly 3 of the first 6 statements are true.
10.  The next two statements are both true.
11.  Exactly 1 of statements 7, 8 and 9 are true.
12.  Exactly 4 of the preceding statements are true.
</pre>


;Task:
When you get tired of trying to figure it out in your head,
write a program to solve it, and print the correct answer or answers.


;Extra credit:
Print out a table of near misses, that is, solutions that are contradicted by only a single statement.
<br><br>