Height of the left tree

In a suspended binary tree, the potential of a vertex is defined as the shortest distance to a vertex with fewer than two children. A tree is considered left if, for each vertex, the potential of the left child is not less than that of the right child. Furthermore, no vertex should have a right child without also having a left child.

The height of a tree is the number of vertices on the longest path from the root to a leaf.

Given a number of vertices N, determine the height of both the tallest and the shortest left tree.

Input

You are provided with a single integer, N, representing the number of vertices in the tree (1 ≤ N ≤ 10_9).

Output

Output two integers: the height of the tallest left tree and the height of the shortest left tree.

Examples