Count the triplets

Very easy

Execution time limit is 2 seconds

Runtime memory usage limit is 128 megabytes

Given three array $a, b$ and $c$ of $n$ integers each. Find the number of triplets $(a_{i}, b_{j}, c_{k})$ such that $a_{i} < b_{j} < c_{k}$ .

Input

First line contains the size of arrays $n (n \leq 1 0^{5})$ . Second line contains elements of array $a$ . Next line contains elements of array $b$ . Last line contains elements of array $c$ .

Output

Print the number of triplets $(a_{i}, b_{j}, c_{k})$ such that $a_{i} < b_{j} < c_{k}$ .

Examples

Input #1

Answer #1

Input #2

Answer #2

Note

In the first test we have triples $(a_{1}, b_{1}, c_{1}), (a_{1}, b_{2}, c_{1})$ and $(a_{1}, b_{2}, c_{2})$ .

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