You are given three arrays A, B, and C. Each array have N elements. You have to find how many triplets (i, j, k) satisfies A[i] + B[j] + C[k] = 0. Note that triplet (1, 1, 2) is considered different from triplet (2, 1, 1).

1 ≤ N ≤ 1000, -1 000 000 000 ≤ A[i], B[i], C[i] ≤ 1 000 000 000

Input

The first line will consist of an integer N.

The second line will consist of N integers separated by space, representing the array A. The third line will consist of N integers separated by space, representing the array B. The fourth line will consist of N integers separated by space, representing the array C.

Output

A single integer as requested in the problem statement.

Example

Input:
2
-6 -1
10 2
-4 -9

Output:
2