Count the departments

Problem

A company chart is a binary tree: each department has at most two sub-departments. Count all the departments in the chart.

Input: Line 1: the tree in level order, values separated by spaces, with null for a missing child. A 'null' alone on line 1 means an empty tree.
Output: One integer: the number of nodes.
Constraints: 0 ≤ number of nodes ≤ 3000
-1000 ≤ each value ≤ 1000

Example 1

Input

1 2 3 4 5

Output

Five departments.

Example 2

Input

null

Output

Try the problem first. Open one hint at a time.

Hint 1

A missing child counts as zero.

Hint 2

Count the node itself plus the count of each side.

Write your Python code, run it on the examples and submit it to hidden tests.