A cavern is mapped as a binary tree over vertical columns: the root is at column 0, a left child at column - 1, a right child at column + 1. Looking straight up from beneath the cavern, in each column you see only the lowest node. For a given column the visible node is the one at the greatest depth; if two nodes in that column share the greatest depth, the visible one is whichever comes later in a level-order (breadth-first, left-to-right) traversal. Report the visible node value for each occupied column, from the left-most column to the right-most.
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 bottom-view node value for each occupied column, left-to-right, 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.