Path decompositions of tournaments

In 1976, Alspach, Mason, and Pullman conjectured that any tournament T$T$ of even order can be decomposed into exactly ex(T)$\operatorname{ex}(T)$ paths, where ex(T) colon equals 12 n-ary sumation v is an element of V(T)|dT+(v)-dT-(v)|$\operatorname{ex}(T)\coloneqq \frac{1}{2}\sum _{v\in V(T)}|d_T<^>+(v)-d_T<^>-(v)|$. We prove this conjecture for all sufficiently large tournaments. We also prove an asymptotically optimal result for tournaments of odd order.