Please use python 3 to solve this question(including the screenshot of your code) thanks! # The Giving Tree of Errors 3.0You are given a binary tree written as a sequence of parent-child pairs. You need to detect any errors that prevent the sequence from being a proper binary tree and print the highest priority error. If you detect no errors, print out the lexicographically smallest S-expression for the tree.## Input FormatInput is read from standard input and has the following characteristics:- It is one line.- Leading or trailing whitespace is not allowed.- The set of pairs is enclosed in parentheses '()', followed by the parent, a comma, followed by the child, followed by a closing parenthesis ')'. Example: (A,B)- All values are single uppercase letters.- Parent-Child pairs are separated by a single space.- The sequence of pairs is not ordered in any specific way.### ExampleInput: (A,B) (B,C) (A,E) (B,D) #### DiagramA tree diagram is presented with the parent node A, branching to children B and E. Node B further branches to nodes C and D.## OutputOutput is written to standard output and must have the following characteristics:- It is one line.- It contains no whitespace.- If errors are present, print the first listed error (e.g., if E3 and E4 are present, print E3).- If no errors are present, print the S-expression representation described below.## ErrorsYou should detect the following errors:- **E1**: Invalid Input Format- **E2**: Duplicate Pair- **E3**: Parent Has More Than Two Children- **E4**: Multiple Roots- **E5**: Input Contains Cycle## S-Expression RepresentationIf the input is a valid tree, you want to print the lexicographically smallest S-expression. "Lexicographically Smallest" simply means "print the children in alphabetical order." Below is a recursive definition of what we want:```S-exp(node) = "({node->val}{S-exp(node->first_child)}{S-exp(node->second_child)})" if node != NULL, "" , node == NULLwhere, first_child->val < second_child->val (lexicographically smaller)```### Sample Inputs and Outputs#### Sample Input #00```(A,B) (B,D) (D,E) (A,C) (C

* The Giving Tree of Errors 3.0 You are given a binary tree written as a sequence of parent-child pairs. You need to detect any errors which prevent the sequence from being a proper binary tree and print the highest priority error. If you detect no errors, print out the lexicographically smallest 5-expression for the tree. Input Format Input is read from standard input and has the following characteristics: • It is one line. Leading or trailing whitespace is not allowed. • Each pair is formatted as an open parenthesis (', followed by the parent, followed by a comma, followed by the child, followed by a closing parenthesis ")'. Example: (A,B) • All values are single uppercase letters. • Parent-Child pairs are separated by a single space. • The sequence of pairs is not ordered in any specific way. Input (A,B) (B,C) (A,E) (B,D) Output Output is written to standard output and must have the following characteristics: • It is one line. • It contains no whitespace. If errors are present, print out the first listed error below (e.g. if E3 and E4 are present, print E3). • If no errors are present, print the S-expression representation described below. Errors You should detect the following errors: Code Туре Invalid Input Format Duplicate Pair E1 E2 E3 Parent Has More than Two Children Multiple Roots Input Contains Cycle E4 ES S-Expression Representation If the input is a valid tree, we want you to print the lexicographically smallest S-Expression. "Lexicographically Smallest" simply means "print the children in alphabetical order." Below is a recursive definition of what we want: S-exp(node) = "({node->val}{S-exp(node->first_child)}{S-exp(node->second_child)})" if node != NULL, = ", node == NULL where, first_child->val < second_child->val (lexicographically smaller) Sample Input #01 Sample Input #00 (A, B) (A,C) (B,D) (D,C) (A, B) (B,D) (D,E) (A,C) {C,F) (E,G) Sample Output #01 ES Sample Output #00 Output #01 Explanation Node D is both a child of B and a parent of C, but Cand B are both child nodes of A. Since D tries to attach itself as parent to a node already above it in the tree, this forms cycle. (A(B(D(E(G))))(C(F))) a YOUR ANSWER