A warehouse rack is modeled as a binary tree hung over a set of vertical columns. The root sits in column 0; a left child sits one column to the left (column - 1) and a right child one column to the right (column + 1). For every column that contains at least one node, report the sum of the node values in that column. List the column totals from the left-most column to the right-most column.

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: the value total of each occupied column, ordered from the left-most column to the right-most, 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

9 18 20 7

4
1 2 null 3

3 2 1