House Robber III

The ninja visits an amusement park but finds himself confused because he wants to ride the rides such that he gets maximum fun. The amusement park has only one entrance that is root.

Each ride has a fun number assigned to it and ninja wants to maximize this fun but there is a rule in the park that no one is allowed to ride two directly connected rides.

As the ninja is smart and good in programming because he did a course from coding ninja, he found immediately that park rides are connected like binary tree where the root is the root of the binary tree. Help the ninja to get the maximum fun this time.

Input Format:

The first line of input contains an integer 'T' representing the number of test cases. Then the test cases follow.

The first line of each test case contains a fun number assigned to each ride in the level order form. The line consists of values of nodes separated by a single space. In case a node is null, we take -1 in its place.

For example, the input for the tree depicted in the below image would be :

4
2 6
1 3 5 7
-1 -1 -1 -1 -1 -1

Explanation:

Level 1 :
The root node of the tree is 4

Level 2 :
Left child of 4 = 2
Right child of 4 = 6

Level 3 :
Left child of 2 = 1
Right child of 2 = 3
Left child of 6 = 5
Right child of 6 = 7

Level 4 :
Left child of 1 = null (-1)
Right child of 1 = null (-1)
Left child of 3 = null (-1)
Right child of 3 = null (-1)
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node(of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.

The input ends when all nodes at the last level are null(-1).

Note:

The above format was just to provide clarity on how the input is formed for a given tree. 

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:

4 2 6 1 3 5 7 -1 -1 -1 -1 -1 -1

Output Format:

For each test case, print the maximum fun that ninja can get from the amusement park.

The output for each test case is printed in a separate line.

Constraints:

1 <= T <= 5
1 <= N <= 5* 10^3
1 <= DATA <= 10^4

Time limit: 1 sec