A binary tree is called perfect if all of its nodes have exactly $0$ or $2$ children and all of its leaves are at the same level. By the size of a perfect tree we mean its number of nodes.

Write a function:

Class solution$\{$public int soultion$($Tree T$)\}$;size of the biggest perfect subtree that can be obtained by removing nodes. For example, given tree T as shown in the previous figure, the funct i should return $7,$ as explained above.

Write an efficient algorithm for the following assumptions:

$$ N is an integer within the range $[1.\mathrm{.}100,000]$;

$$ the height of tree T $($number of edges on the longest path from root to leaf$)$ is within the range $[0\mathrm{.}800].$

Technical details

A binary tree can be specified using a pointer data structure. Assume that the following declarations are given:

class Tree $\{$

public int x;

public Tree l;

public Tree r;

$\}$

An empty tree is represented by an empty pointer $($denoted by null$).$ A non$-$empty tree is represented by a pointer to an object representing its root. The attribute holds the integer contained in the root, whereas attributes $1$ and r hold the left and right subtrees of the binary tree, respectively.

For the purpose of entering your own test cases, you can denote a tree recursively in the following way. An empty binary tree is denoted by None. A non$-$empty tree is denoted as $($X$,$ L$,$ R$),$ where X is the value contained in the root and L and R denote the left and right subtrees, respectively. The tree from the above figure can be denoted as:

$(1,(2,$ None, $(4,$ None, None$)),(3,(5,(7,$ None, None$),(8,$ None, None$)),(6,(9,$ None, None$),(10,(11,$ None, None$),$

None$))))$

Write java$8$ solution