class MyCalendarTwo {
    private Bst bst = null;
    public MyCalendarTwo() {        
    }
    
    public boolean book(int start, int end) {
        return validateAndInsert(start, end);
    }
    
    /**
     * insert the node into #bst only if the given interval is not triple overlapping with existing evetns. 
     */
    private boolean validateAndInsert(int start, int end) {
        if(findOverlapCount(bst, start,end) >= 2) {
            return false;
        }
        insert(start,end);
        return true;
    }
    
    /**
     * Do inorder traversal in that process keep track of the count of
     * overlapping intervals with the input interval.
     * Stop iterating 
     * 1) Overlapping count reaches 2 
     * 2) Or current node's start is < end
     **/
    private int findOverlapCount(Bst root, int start, int end) {
        if(root == null) {
            return 0;
        }
        int lCount = findOverlapCount(root.left, start, end);
        // Current element's start is 
        if(root.start>end || lCount >=2 ) {
            return lCount;
        }
        int cCount = isOverlapping(root, start, end)?1:0;
        int rCount = findOverlapCount(root.right, start, end);
        return lCount + cCount + rCount;
    }
    
    /**
     * Insert given interval into BST.
     **/
    private void insert(int start, int end) {
        if(bst == null) {
            bst = new Bst(start, end, null, null);
            return;
        }
        Bst itr = bst;
        Bst previous = itr;
        while(itr != null) {
            previous = itr;
            if(start <= itr.getStart()) {
                itr = itr.getLeft();
            } else {
                itr = itr.getRight();
            }
        }
        Bst newNode = new Bst(start, end, null, null);
        if(start<=previous.getStart()) {
            previous.setLeft(newNode);
        } else {
            previous.setRight(newNode);
        }        
    }
    
    private boolean isOverlapping(Bst node, int s2, int e2) {
        int s1 = node.start;
        int e1 = node.end;        
        if(s1<e2 && s2 < e1) {
            return true;
        }
        return false;
    }
}

class Bst {
        int start;
        int end;
        Bst left;
        Bst right;
        public Bst(int start, int end, Bst left, Bst right) {
            this.start = start;
            this.end = end;
            this.left = left;
            this.right = right;
        }
        public int getStart() {
            return start;
        }
        public int getEnd() {
            return end;
        }
        public Bst getLeft() {
            return left;
        }
        public Bst getRight() {
            return right;
        }
        public void setLeft(Bst left) {
            this.left = left;
        }
        public void setRight(Bst right) {
            this.right = right;
        }
}
/**
 * Your MyCalendarTwo object will be instantiated and called as such:
 * MyCalendarTwo obj = new MyCalendarTwo();
 * boolean param_1 = obj.book(start,end);
 */