Definite Integration

If \(\int\limits_{{1 \over 3}}^3 {|{{\log }_e}x|dx = {m \over n}{{\log }_e}\left( {{{{n^2}} \over e}} \right)}\), where m and n are coprime natural numbers, then \({m^2} + {n^2} - 5\) is equal to _____________.