31768번 - Smaller Averages 다국어

문제

Bessie has two arrays of length $N$ (1ドル \le N \le 500$). The $i$-th element of the first array is $a_i$ (1ドル \le a_i \le 10^6$) and the $i$-th element of the second array is $b_i$ (1ドル \le b_i \le 10^6$).

Bessie wants to split both arrays into non-empty subarrays such that the following is true.

1. Every element belongs in exactly 1 subarray.
2. Both arrays are split into the same number of subarrays. Let the number of subarrays the first and second array are split into be $k$ (i.e. the first array is split into exactly $k$ subarrays and the second array is split into exactly $k$ subarrays).
3. For all 1ドル \le i \le k,ドル the average of the $i$-th subarray on the left of the first array is less than or equal to the average of the $i$-th subarray on the left of the second array.

Count how many ways she can split both arrays into non-empty subarrays while satisfying the constraints modulo 10ドル^9+7$. Two ways are considered different if the number of subarrays are different or if some element belongs in a different subarray.

입력

The first line contains $N$.

The next line contains $a_1,a_2,...,a_N$.

The next line contains $b_1,b_2,...,b_N$.

출력

Output the number of ways she can split both arrays into non-empty subarrays while satisfying the constraints modulo 10ドル^9+7$.

제한

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