Count the triplets

Input

The first line contains the size of the arrays $n (n \leq 1 0^{5})$ n~(n \le 10^5).

The second line contains the elements of array $a$ .

The third line contains the elements of array $b$ .

The fourth line contains the elements of array $c$ .

Output

Print the number of triplets $(a_{i}, b_{j}, c_{k})$ (a_i, b_j, c_k) that satisfy the condition $a_{i} < b_{j} < c_{k}$ a_i < b_j < c_k.

Examples

Example 1

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Example 2

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Note

In the first test case, the valid triplets are $(a_{1}, b_{1}, c_{1}), (a_{1}, b_{2}, c_{1})$ (a_1, b_1, c_1), (a_1, b_2, c_1) and $(a_{1}, b_{2}, c_{2})$ (a_1, b_2, c_2).