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

Input
Output
4 13 6 8 3 1 3 5 8 9 15 7 5
7

Explanation

 

Constraints

Time limit: 4.8 seconds

Memory limit: 512 MB

Output limit: 1 MB

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