Given an array of integers. Create a Binary Search Tree from these numbers. If the inserted value equals to the current node, insert it to the right subtree.

Write a method MinDepth that finds the minimum depth of a tree. The minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node.

Write the code according to the next interface:

class TreeNode

{

public:

int val;

TreeNode *left;

TreeNode *right;

TreeNode(int x) : val(x), left(NULL), right(NULL) {}

};

class Tree

{

public:

TreeNode *head;

Tree() : head(NULL) {};

void Insert(int val); // Insert number val to Binary Search Tree

int MinDepth(void); // Return the minimum depth of a Binary Search Tree

};

You can create (use) additional methods if needed.

Input

The first line contains number n (1 ≤ n ≤ 100). The second line contains n integers.

Output

Create the Binary Search Tree from input data. Find and print its minimum depth.