You are given a sequence of n positive integers a₁, _a2, ….., a_n where 1 ≤ n ≤ 1000 and 1 ≤ a_i ≤ 2³⁰-1. You have to make the sequence strictly increasing by performing following operation zero or more times:

• Choose an integer a_i from the sequence where 1 ≤ i ≤ n.
• And perform a_i = a_i | (1 << p) where 0 ≤ p ≤ 59. Here | denotes bitwise or operation and 1 << p means 2^p.

Now you need to find the minimum number of operations needed to convert the given sequence to a strictly increasing sequence. If it is not possible to make the sequence strictly increasing then output -1.

The first line contains the number of test cases T where 1 ≤ T ≤ 10. Then T test cases follow. The first line of each test case contains n (1 ≤ n ≤ 1000) and the second line contains the sequence of n positive integers. The sum of n over all test cases is not larger than 5000.

Print the case number in a single line followed by the minimum number of operations needed or -1 if there is no solution.