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class Node:
    def __init__(self, data):
        self.children = []
        self.data = data

def find_node(root, target_data):
    if root is None:
        return None

    if root.data == target_data:
        return root

    for child in root.children:
        result = find_node(child, target_data)
        if result:
            return result

    return None

def find_path(root, target, path):
    if root is None:
        return False

    path.append(root)

    if root.data == target.data:
        return True

    for child in root.children:
        if find_path(child, target, path):
            return True

    path.pop()
    return False

def find_lca(root, node1, node2):
    path_to_node1 = []
    path_to_node2 = []

    if not (find_path(root, node1, path_to_node1) and find_path(root, node2, path_to_node2)):
        return None

    i = 0
    while i < len(path_to_node1) and i < len(path_to_node2):
        if path_to_node1[i].data != path_to_node2[i].data:
            break
        i += 1

    return path_to_node1[i - 1]

# Example usage
# Build the tree:
#        1
#       /|\
#      2 3 4
#     / \
#    5   6

root = Node(1)
root.children = [Node(2), Node(3), Node(4)]
root.children[0].children = [Node(5), Node(6)]

node1 = root.children[2]  # Node 2
node2 = root.children[0].children[0]  # Node 4

lca = find_lca(root, node1, node2)
if lca:
    print("LCA of", node1.data, "and", node2.data, "is:", lca.data)
else:
    print("LCA not found")

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class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def insert(root, val):
    if root is None:
        return TreeNode(val)

    if val < root.val:
        root.left = insert(root.left, val)
    else:
        root.right = insert(root.right, val)

    return root

def preorder_traversal(root):
    if root:
        print(root.val, end=" ")
        preorder_traversal(root.left)
        preorder_traversal(root.right)

# Example usage
num_array = [5, 2, 8, 1, 3, 6, 9]

root = None
for num in num_array:
    root = insert(root, num)

print("Pre-order traversal:")
preorder_traversal(root)

'''
      5
 2        8
1  3    6   9
'''

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a = [0, 1, 3, 5, 2, 4, 6, 8, 7]
n = 8
t = [0] * 100

def build(id, l, r):
    if l == r:
        t[id] = a[l]
        print(f"{id}, {l}, {r}, {t[id]}")
        return
    
    mid = (l + r) // 2
    build(id * 2, l, mid)
    build(id * 2 + 1, mid + 1, r)
    
    t[id] = t[id * 2] + t[id * 2 + 1]
    print(f"{id}, {l}, {r}, {t[id]}")

def get(id, l, r, u, v):
    if r < u or v < l:
        return 0
    if u <= l and r <= v:
        print(f"->{id}, {l}, {r}, {t[id]}")
        return t[id]
    
    mid = (l + r) // 2
    t1 = get(id * 2, l, mid, u, v)
    t2 = get(id * 2 + 1, mid + 1, r, u, v)
    print(f"{id}, {l}, {r}, {t1 + t2}")
    
    return t1 + t2

def update(id, l, r, pos, val):
    if pos < l or r < pos:
        return
    if l == r:
        t[id] = val
        a[l] = val
        return
    
    mid = (l + r) // 2
    update(id * 2, l, mid, pos, val)
    update(id * 2 + 1, mid + 1, r, pos, val)
    t[id] = t[id * 2] + t[id * 2 + 1]

build(1, 1, n)
print("====")
print(get(1, 1, n, 2, 5))
print("======")
update(1, 1, n, 4, 10)
print(get(1, 1, n, 2, 5))