Orders in a number range

Problem

A binary search tree holds order numbers. Given low and high, print how many keys are between them, inclusive, and the sum of those keys.

Input: Line 1: the tree in level order, keys separated by spaces, with # for a missing child. The children of a missing node are not listed, and trailing # may be left out. A single # is an empty tree. Line 2: low and high separated by a space.
Output: Two integers: the count and the sum.
Constraints: 0 ≤ number of nodes ≤ 300
1 ≤ low ≤ high ≤ 1000000, keys all different

Example 1

Input

8 3 10 1 6 # 14 # # 4 7 13
4 10

Output

5 35

Example 2

Input

8 3 10 1 6 # 14 # # 4 7 13
20 30

Output

0 0

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

Hint 1

Skip the left subtree when the node is not larger than low, and the right subtree when it is not smaller than high.

Hint 2

A generator of the keys in range feeds len and sum.

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