This time Laltu wanted the question to be straightforward. So, given 3 1-indexed sorted arrays (A[, B[], C[])], find the number of triplets 1 ≤ i ≤ j ≤ k, such that: A[i] ≤ B[j] ≤ C[k]. Note that i, j and k don’t exceed the size of respective arrays.
For example, Arrays: A = [1, 2, 3, 4] B = [5, 6, 7, 8] C = [9, 10, 11, 12]
The triplet (i, j, k) = (1, 2, 3) has to be considered because: A[1] ≤ B[2] ≤ C[3].
First line contains T, the number of test cases. Each test case consists of: P, the length of first array. The next line will consist of P integers. Q, the length of second array. The next line will consist of Q integers. R, the length of third array. The next line will consist of R integers.
For each test case print the required answer in one line.
*Constraints*
The possible triplets (i, j, k) are: (1, 1, 1) (1, 1, 2) (1, 1, 3) (1, 2, 2) (1, 2, 3) (1, 3, 3)
## Input
First line contains T, the number of test cases. Each test case consists of: P, the length of first array. The next line will consist of P integers. Q, the length of second array. The next line will consist of Q integers. R, the length of third array. The next line will consist of R integers.
## Output
For each test case print the required answer in one line.*Constraints* 1 ≤ T ≤ 3 1 ≤ P, Q, R ≤ 105 - 109 ≤ Elements of arrays ≤ 109
[samples]
## Note
The possible triplets (i, j, k) are: (1, 1, 1) (1, 1, 2) (1, 1, 3) (1, 2, 2) (1, 2, 3) (1, 3, 3)
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case:
- Let $ P, Q, R \in \mathbb{Z}^+ $ denote the lengths of arrays $ A $, $ B $, and $ C $, respectively.
- Let $ A = (a_1, a_2, \dots, a_P) $, $ B = (b_1, b_2, \dots, b_Q) $, $ C = (c_1, c_2, \dots, c_R) $ be three 1-indexed sorted arrays of integers.
**Constraints**
1. $ T \geq 1 $
2. For each test case:
- $ 1 \leq P, Q, R \leq \text{some upper bound (implied by context)} $
- $ a_1 \leq a_2 \leq \dots \leq a_P $
- $ b_1 \leq b_2 \leq \dots \leq b_Q $
- $ c_1 \leq c_2 \leq \dots \leq c_R $
**Objective**
Count the number of triplets $ (i, j, k) \in \{1, \dots, P\} \times \{1, \dots, Q\} \times \{1, \dots, R\} $ such that:
$$
a_i \leq b_j \leq c_k
$$