Just Stalling

문제

Farmer John has $NN$ cows ($1\le N\le 201\backslash le\; N\; \backslash leq\; 20$) of heights $a_1\dots a_{N}a\_1\; \backslash ldots\; a\_N$. His barn has $NN$ stalls with max height limits $b_1\dots b_{N}b\_1\; \backslash ldots\; b\_N$ (so for example, if $b_5=17b\_5\; =\; 17$, then a cow of height at most $1717$ can reside in stall $55$). 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?

입력

The first line contains $NN$. The second line contains $NN$ space-separated integers $a_1,a_2,\dots ,a_{N}a\_1,a\_2,\backslash ldots,a\_N$. The third line contains $NN$ space-separated integers $b_1,b_2,\dots ,b_{N}b\_1,b\_2,\backslash ldots,b\_N$. All heights and limits are in the range $[1,{10}^9][1,10^9]$.

출력

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++.