Given a binary tree, return its maximum depth.

The depth of a binary tree is the number of nodes from the root node to any of the leaf nodes. The maximum depth is the maximum of the depths across all the paths.

Example

Testing

Input Format

The first line contains an integer T denoting the number of test cases.

For each test case, the input has 2 lines:

• The first line contains an integer n denoting the number of nodes in the tree (including the NULL nodes).
• The second line contains n space-separated integers that will form the binary tree. The integers follow level order traversal of the tree where -1 indicates a NULL node.

Output Format

For each test case, the output has an integer denoting the maximum depth of the tree.

Sample Input

5
12
1 2 3 4 5 6 -1 -1 -1 7 -1 8
7
1 2 -1 4 -1 5 6
7
8 -1 9 -1 10 11 12
5
28 14 11 -1 48
1
6

Expected Output

4
4
4
3
1

Constraints

1 <= T <= 10
1 <= n <= 105
1 <= node value <= 104