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Distances in Binary Search Trees

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Distances in Binary Search Trees
Given an array representing values to be added to an empty binary search tree in order, and a pair of these values, return the shortest path distance between these values in the tree after all values have been inserted.

Input format:
line 1: [node values for input tree]
line 3: [node1] [node2]

Examples

Input:
3 1 5 7 2 4
1 7
Output:
3
The shortest path from 1 to 7 is through their common ancestor 3.

Input:
3 1 5 7 2 4
3 4
Output:
2
This is because in the completed tree, 5 is a child of 3, and 4 is a child of 5.

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