Convert Sorted Doubly Linked List To Binary Search Tree

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1. Convert a sorted Doubly-Linked List to a Balanced Binary Search Tree in place.
2. The previous and next pointers in nodes are to be used as left and right pointers respectively in converted Binary Search Tree. 
3. The tree must be constructed in-place (No new node should be allocated for tree conversion) 

Input Format

Input is managed for you.

Output Format

Output is managed for you.

Constraints

0 <= Number of Nodes <= 10^9
-10^9 <= value of Node data <= 10^9

Notice

Try First, Check Solution later

1. You should first read the question and watch the question video.
2. Think of a solution approach, then try and submit the question on editor tab.
3. We strongly advise you to watch the solution video for prescribed approach.

Example

Input
7
1 2 3 4 5 6 7
Output
2 -> 4 <- 6
1 -> 2 <- 3
. -> 1 <- .
. -> 3 <- .
5 -> 6 <- 7
. -> 5 <- .
. -> 7 <- .
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