Probability that X is less than Y for i.i.d. variables

Let $X$ and $Y$ be continuous random variables with the joint probability density function

$$f(x,y)=\begin{cases}e^{(x+y)}, & -\infty<x,y<0,\ 0, & \text{otherwise.}\end{cases}$$

Then $P(X<Y)=$ ____________________