E. Best Subsequence
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an integer array $$$a$$$ of size $$$n$$$.

Let's define the value of the array as its size minus the number of set bits in the bitwise OR of all elements of the array.

For example, for the array $$$[1, 0, 1, 2]$$$, the bitwise OR is $$$3$$$ (which contains $$$2$$$ set bits), and the value of the array is $$$4-2=2$$$.

Your task is to calculate the maximum possible value of some subsequence of the given array.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i < 2^{60}$$$).

Output

For each test case, print the maximum possible value of some subsequence of the given array.

Example
Input
4
3
0 0 0
4
1 0 1 2
1
5
8
7 1 48 14 13 8 7 6
Output
3
2
0
3