You are given an array $$$a$$$ of length $$$n$$$. The score of $$$a$$$ is the MEX$$$^{\dagger}$$$ of $$$[a_1+a_2,a_2+a_3,\ldots,a_{n-1}+a_n]$$$. Find the minimum score of $$$a$$$ if you are allowed to rearrange elements of $$$a$$$ in any order. Note that you are not required to construct the array $$$a$$$ that achieves the minimum score.

$$$^{\dagger}$$$ The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array. For instance:

The MEX of $$$[2,2,1]$$$ is $$$0$$$, because $$$0$$$ does not belong to the array.
The MEX of $$$[3,1,0,1]$$$ is $$$2$$$, because $$$0$$$ and $$$1$$$ belong to the array, but $$$2$$$ does not.
The MEX of $$$[0,3,1,2]$$$ is $$$4$$$ because $$$0$$$, $$$1$$$, $$$2$$$, and $$$3$$$ belong to the array, but $$$4$$$ does not.

Input

The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2\le n\le 2\cdot10^5$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 2\cdot 10^5$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, output the minimum score of $$$a$$$ after rearranging the elements of $$$a$$$ in any order.

Note

In the first test case, it is optimal to rearrange $$$a$$$ as $$$[0,0]$$$, the score of this array is the MEX of $$$[0+0]=[0]$$$, which is $$$1$$$.

In the second test case, it is optimal to rearrange $$$a$$$ as $$$[0,1,0]$$$, the score of this array is the MEX of $$$[0+1,1+0]=[1,1]$$$, which is $$$0$$$.

Mex Master

Examples