Evaluate the integral ${\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{\frac{\sqrt[\phantom{2}]{2}}{2}}{}}}{\displaystyle \underset{x}{\overset{\sqrt[\phantom{2}]{1-x^2}}{}}}{e}^{-x^2-y^2}dydxdz$ using cylindrical coordinates. Enter an exact answer. Type pi to enter $$ and e to enter the base of the natural exponential function $e.$

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