Given the system\[\lfloor b\rfloor+ \lceil a\rceil+ \{c\}=16 \] \[\lfloor c\rfloor+ \lceil b\rceil +\{a\}=11.3 \] \[\lfloor a\rfloor+ \lceil c\rceil +\{b\}=9.7 ,\] what is \(a+b+c\)?

Note:

\(\lfloor x\rfloor \) Represents the floor function, which takes the greatest integer smaller or equal to x.

\(\lceil x\rceil \) represents the ceiling function, which takes the smallest integer greater or equal to x.

Finally, \(\{x\}\) represents the fractional part function.

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