A company org chart is modeled as a binary tree: the root is the CEO and every node's children are that person's direct reports. Tier 0 is the CEO's tier, tier 1 holds the CEO's direct reports, and so on. Report the number of people on each tier, from the top tier down to the deepest.

Input format

Line 1: an integer n, the number of tokens on the next line.

Line 2: n space-separated tokens describing a binary tree in level-order (breadth-first). The first token is the root's value. Reading left to right, keep a queue of already-created nodes; for each node taken from the front of the queue, the next two tokens are its left child then its right child, where the token null marks a missing child. Only non-null children are added to the queue. Trailing null tokens for absent children at the deepest level may be omitted. Every node value is an integer.

Output format

A single line with the headcount of each tier from tier 0 downward, space-separated.

Constraints

• 1 <= n <= 129
• The tree has at least 1 and at most 40 nodes.
• Each node value is an integer with -1000 <= value <= 1000.

7
3 9 20 null null 15 7

1 2 2

1
5

1