Directed Graphs and Network Flows · Hard problem

In the $5$-team tournament ($1\to2$, $2\to3$, $3\to1$, $1\to4$, $4\to2$, $3\to4$, $1\to5$, $5\to2$, $5\to3$, $4\to5$), how many Hamiltonian paths does it have — directed paths visiting all $5$ teams, each exactly once, always moving winner-to-loser?