There are 5 Integer Arrays and each of them contains no more than 300 integers whose value are between -100,000,000 and 100,000,000, You are to find how many such groups (i,j,k,l,m) can make A[0][i]+A[1][j]+A[2][k]+A[3][l]+A[4][m]=0. Maybe the result is too large, you only need tell me the remainder after divided by 1000000007.
Input
In the first line, there is an Integer T(0<T<20), means the test cases in the input file, then followed by T test cases.
For each test case, there are 5 lines Integers, In each line, the first one is the number of integers in its array.
Output
For each test case, just output the result, followed by a newline character.