Given an array of N integers A₁, A₂, A₃…A_N. If you randomly choose two indexes i ,j such that 1 ≤ i < j ≤ N, what is the expected value of A_i | A_j?

Input

First line contains an integer T, the number of test cases. Each test case consists of two lines. First line denotes the size of array, N and second line contains N integers forming the array.
1 ≤ T ≤ 10
2 ≤ N ≤ 100,000
0 ≤ Ai < 2³¹

Output

For each test case, print the answer as an irreducible fraction. Follow the format of the sample output.
The fraction p/q (p and q are integers, and both p ≥ 0 and q > 0 holds) is called irreducible, if there is no such integer d > 1 that divides both p and q separately.

Example

Input:
2
2
0 0
3
1 2 3
Output:
0/1
3/1