Just Stalling

Farmer John has $N$ cows ($1\le N \leq 20$) of heights $a\_1 \ldots a\_N$. His barn has $N$ stalls with max height limits $b\_1 \ldots b\_N$ (so for example, if $b\_5 = 17$, then a cow of height at most $17$ can reside in stall $5$). In how many distinct ways can Farmer John arrange his cows so that each cow is in a different stall, and so that the height limit is satisfied for every stall?

The first line contains $N$. The second line contains $N$ space-separated integers $a\_1,a\_2,\ldots,a\_N$. The third line contains $N$ space-separated integers $b\_1,b\_2,\ldots,b\_N$. All heights and limits are in the range $\[1,10^9]$.

The number of ways Farmer John can place each cow into a different stall such that the height limit is satisfied for every stall. Note that the large size of the output might require the use of a 64-bit integer, like a "long long" in C++.