Increasing triplets

Given 3 arrays a, b, and c of length n, you are asked to find the number of triplets (i, j, k) such that .

Input

The first line of the input contains a single integer n (1 ≤ n ≤ ).

The next line contains n integers (0 ≤ ≤ ).

The second line contains n integers (0 ≤ ≤ ).

Finally, the third line contains n integers (0 ≤ ≤ ).

Output

The program should print the number of increasing triplets.

Examples

Explanation