Find the smallest difference in BST

Given a binary search tree, you are asked to find the smallest difference between two different elements of the BST.

Input

The input is handled automatically, you don’t need to do anything. All the values of the nodes are positive integers that don’t exceed . It’s guaranteed that the input BST tree is valid and has more than 2 nodes.

Output

The program should print the minimum absolute smallest difference between two elements in the BST.

Examples

Input
Output
4 1 10 3 6
2
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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