Arranging game levels

Hyunwook makes games as a hobby, and today he sketched a simple design. The game has $N$ levels, and the player earns a fixed number of points for clearing each one. Every level has a fixed list of levels that the player may move to after clearing it, and the player picks one of them.

The design is as follows.

1. There is one starting level.
2. A way to reach any other level from the starting level always exists, and it is unique.
3. Clearing level $i$ gives the player $S_i$ points.
4. Each level $i$ also has a value $K_i$, the cumulative score the designer intends the player to hold right after clearing level $i$. It is the sum of the clear scores of every level on the way from the starting level to level $i$, including level $i$ itself.
5. If level $i$ has to be cleared after level $j$, then $S_i > S_j$ must hold. The game only moves toward levels that award more points.

Hyunwook wants to know how many level arrangements satisfy these rules. Write a program that counts the arrangements of the $N$ levels that match all of the given $S_i$ and $K_i$.

The first line contains the number of levels $N$ ($1 \le N \le 3 \times 10^5$).

The second line contains $S_1, S_2, \dots, S_N$ ($1 \le S_i \le 10^9$), separated by spaces.

The third line contains $K_1, K_2, \dots, K_N$ ($1 \le K_i \le 10^9$), separated by spaces.

Print the number of arrangements that satisfy the given $S_i$ and $K_i$, modulo $10^9 + 7$. Two arrangements count as the same one when every level has the same list of next levels in both, where the order inside a list does not matter.

The first example has exactly one valid arrangement. Level 1 is the starting level, and after clearing it the player chooses between level 2 and level 3. The second example has no valid arrangement.