You are given two arrays $a$ and $b$ each consisting of $n$ integers. All elements of $a$ are pairwise distinct.

Find the number of ways to reorder $a$ such that $a_i \gt b_i$ for all $1 \le i \le n$, modulo $10^9 + 7$.

Two ways of reordering are considered different if the resulting arrays are different.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^{5}$) — the length of the array $a$ and $b$.

The second line of each test case contains $n$ distinct integers $a_1$, $a_2$, $\ldots$, $a_n$ ($1 \le a_i \le 10^9$) — the array $a$. It is guaranteed that all elements of $a$ are pairwise distinct.

The second line of each test case contains $n$ integers $b_1$, $b_2$, $\ldots$, $b_n$ ($1 \le b_i \le 10^9$) — the array $b$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^{5}$.

Output

For each test case, output the number of ways to reorder array $a$ such that $a_i \gt b_i$ for all $1 \le i \le n$, modulo $10^9 + 7$.

Samples

5
6
9 6 8 4 5 2
4 1 5 6 3 1
3
4 3 2
3 4 9
1
2
1
3
2 3 4
1 3 3
12
2 3 7 10 23 28 29 50 69 135 420 1000
1 1 2 3 5 8 13 21 34 55 89 144

32
0
1
0
13824