The potential of a vertex in a suspended binary tree is the shortest distance to a vertex with fewer than two children. A tree is called left if, for each vertex, the left child has a potential not less than that of the right child. Furthermore, there must not be any vertex that has a right child but no left child.
The height of a tree is the number of vertices on the longest path from the root to a leaf.
Given the number of vertices , determine the height of both the tallest and the shortest left tree.
A single integer is given: the number of vertices in the tree (1 \leq N \leq 10^9).
Output two integers: the height of the tallest left tree and the height of the shortest left tree.
Example 1