You are given a 0-indexed integer array order of length n, a permutation of integers from 1 to n representing the order of insertion into a binary search tree.

A binary search tree is defined as follows:

• The left subtree of a node contains only nodes with keys less than the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.
• Both the left and right subtrees must also be binary search trees.

The binary search tree is constructed as follows:

• order[0] will be the root of the binary search tree.
• All subsequent elements are inserted as the child of any existing node such that the binary search tree properties hold.

Return the depth of the binary search tree.

A binary tree's depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

 

Example 1:

Input: order = [2,1,4,3]
Output: 3
Explanation: The binary search tree has a depth of 3 with path 2->3->4.

Example 2:

Input: order = [2,1,3,4]
Output: 3
Explanation: The binary search tree has a depth of 3 with path 2->3->4.

Example 3:

Input: order = [1,2,3,4]
Output: 4
Explanation: The binary search tree has a depth of 4 with path 1->2->3->4.

 

Constraints:

• n == order.length
• 1 <= n <= 105
• order is a permutation of integers between 1 and n.