Justice For Everyone

Suppose you have $n$ pairwise different numbers on a desk, denoted by $a_1, a_2, \ldots, a_n$ (order matters). In one turn, you can choose two different indices $i_1 < i_2$ and simultaneously increase $a_{i_1}$ and $a_{i_2}$ by one. The only condition is that the numbers on the desk must be pairwise different at every moment. Your task is to find the number of ways to obtain pairwise different numbers $b_1, b_2, \ldots, b_n$ (in exactly this order). Since this number can be very large, print it modulo $998\,244\,353$.

The first line contains a single integer $n$ ($1 \le n \le 30$). The second and third lines each contain $n$ space-separated integers: the arrays $a_i$ and $b_i$, respectively ($1 \le a_i, b_i \le 200$). All $a_i$ are pairwise different, and so are all $b_i$.

Print the answer modulo the prime number $998\,244\,353$.

In the first sample, the only way is to perform the operations in the order $\{2, 3\}, \{1, 3\}, \{1, 2\}$. In the third sample, you can perform the three operations $\{1, 2\}, \{2, 3\}, \{1, 3\}$ in any order.