Unsupported operand type(s) for +=: 'int' and 'NoneType'

Unsupported operand type(s) for +=: 'int' and 'NoneType' 

Ошибка при попытке найти сумму всех узлов. Почему?

class Node(object):

    def __init__(self, root):
        self.right = None
        self.left = None
        self.root = root

    def put(self, data):
        if self.root:
            if data < self.root:
                if self.left is None:
                    self.left = Node(data)
                else:
                    self.left.put(data)
            if data > self.root:
                if self.right is None:
                    self.right = Node(data)
                else:
                    self.right.put(data)
        else:
            self.root = data

    def printree(self):
        if self.left:
            self.left.printree()
        print(self.root)
        if self.right:
            self.right.printree()

    def sum_tree(self):
        tree_sum = 0
        if self.left:
            tree_sum += self.left.sum_tree()
        if self.right:
            tree_sum += self.right.sum_tree()
        return tree_sum


def mass():  
   with open('_input_.txt') as inp:
       res = list(map(int, inp.read()[1:].split()))
   return res[1:]

arr = mass()
arr.sort()
d = Node(arr[len(arr)//2])
for el in arr:
    d.put(el)
d.printree()
print(d.sum_tree())