A binary tree is symmetric if the left subtree is a mirror reflection of the right subtree: their shapes match and mirrored positions hold equal values. Decide whether the given tree is symmetric.
Input format
One line: the binary tree as a level-order array.
The tree is encoded on ONE line as a space-separated level-order (breadth-first) array. The token null marks a missing child; the children of a null are omitted from the array. An empty tree is written as the single token null.
Output format
Print YES if the tree is symmetric, otherwise NO. An empty tree is considered symmetric.
Constraints
- The tree has between 0 and 1000 nodes.
- Each node value is an integer with absolute value at most 1000.