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# Question 1: Locking the Tree of Space
# You have a world map represented as an M-Ary tree (sample tree below):

# You need to define three operations on it:
# lock(X, uid)
# unlock(X, uid)
# upgradeLock(X, uid)
# Where X is the name of a node in the tree (which is unique), and uid is the user performing the operation.
# Definitions for the Operations:
# Lock(X, uid):
# Lock takes exclusive access on the subtree rooted at X. Once lock(X, uid) succeeds:
# lock(A, anyUserId) should fail (returns false), where A is a descendant of X.
# lock(B, anyUserId) should fail (returns false), where X is a descendant of B.
# Lock operation cannot be performed on a node that is already locked, i.e., lock(X, anyUserId) should fail (returns false).
# Unlock(X, uid):
# Unlock reverts what was done by the lock operation. It can only be called on the same node on which user uid had called a lock before. Returns true if successful.
# UpgradeLock(X, uid):
# This helps the user uid upgrade their lock to an ancestor node. It is only possible if the node X already has locked descendants and all of them are locked by the same user uid. Upgrade should fail if there is any node which is a descendant of X that is locked by a different user. A successful upgrade will "lock" the node. UpgradeLock must not violate the consistency model required by Lock/Unlock.
# Notes:
# The number of nodes in the tree, N, is very large, so optimize the time complexity for the above algorithms.
# Input Format:
# The first line contains the number of nodes in the tree (N).
# The second line contains the number of children per node (m in an m-ary tree).
# The third line contains the number of queries (Q).
# Next N lines contain the NodeName (string) in the m-Ary Tree.
# The next Q lines contain queries in the format: OperationType NodeName UserId.
# Operation Type:
# 1 for Lock
# 2 for Unlock
# 3 for UpgradeLock
# NodeName: The name of any node (unique) in the m-Ary Tree.
# UserId: An integer representing a unique user.
# Example Input:
# 7
# 2
# 3
# World
# Asia
# Africa
# China
# India
# South Africa
# Egypt
# 1 China 9
# 2 India 9
# 3 Asia 9


# This input represents a 2-ary tree with 7 nodes as follows:
# World
# / <br/># Asia Africa
# / \ / <br/># China India South Africa Egypt


# Additional Notes:
# The tree is always fully balanced.
# Constraints:
# (1 < N < 5 \times 10^5)
# (1 < m < 30)
# (1 < Q < 5 \times 10^5)
# (1 < \text{length of NodeName} < 20)
# Optimize the time complexity:
# Lock: (O(\log_m N))
# Unlock: (O(\log_m N))
# UpgradeLock: (O(\text{numberOfLockedNodes} \times \log_m N))
# The lock operation on an already locked node should fail.
# Once UpgradeLock(X, uid) succeeds on X, it is equivalent to X being locked by uid. As per the definition, Lock(A/B, anyUser) should fail, and Unlock(X, uid) should also work.
# Upgrade lock operation on a node having no locked descendants should fail, and upgrade lock on an already locked node should also fail.


import sys


class Node:
def init(self, val):
self.val = val # Node value (name)
self.uid = None # User ID who locked the node
self.parent = None # Reference to parent node
self.children = [] # List of child nodes
self.isLocked = False # Lock status
self.lockedDescendantCount = 0 # Number of locked descendants


class Tree:
def init(self, n, m, node_list, queries):
self.node_list = []
self.node_map = {}

# Create node instances and map node names to instances
for name in node_list:
node = Node(name)
self.node_list.append(node)
self.node_map[name] = node

# Assign children to each node based on m-ary tree properties
for i in range(n):
for j in range(m):
child_index = m * i + j + 1
if child_index < n:
self.node_list[i].children.append(self.node_list[child_index])
self.node_list[child_index].parent = self.node_list[i]

self.root = self.node_list[0]

# Process queries
self.processed_queries = [query.strip().split() for query in queries]

def lock(self, node, uid):
# Check if node is already locked
if node.isLocked:
return False

# Check if any ancestors are locked
if self.isAncestorLocked(node):
return False

# Check if any descendants are locked
if node.lockedDescendantCount > 0:
return False

# Lock the node
node.isLocked = True
node.uid = uid

# Update ancestors' lockedDescendantCount
parent = node.parent
while parent:
parent.lockedDescendantCount += 1
parent = parent.parent

return True

def unlock(self, node, uid):
# Check if node is locked by uid
if not node.isLocked or node.uid != uid:
return False

# Unlock the node
node.isLocked = False
node.uid = None

# Update ancestors' lockedDescendantCount
parent = node.parent
while parent:
parent.lockedDescendantCount -= 1
parent = parent.parent

return True

def upgrade(self, node, uid):
# Check if node is already locked
if node.isLocked:
return False

# Check if any ancestors are locked
if self.isAncestorLocked(node):
return False

# Check if there are any locked descendants
if node.lockedDescendantCount == 0:
return False # No locked descendants to upgrade

# Collect all locked descendants
locked_descendants = []
if not self.collectLockedDescendants(node, uid, locked_descendants):
return False # Cannot upgrade due to locks by other users

# Unlock all locked descendants
for descendant in locked_descendants:
descendant.isLocked = False
descendant.uid = None
# Update ancestors' lockedDescendantCount
parent = descendant.parent
while parent:
parent.lockedDescendantCount -= 1
parent = parent.parent

# Lock the node
node.isLocked = True
node.uid = uid

# Update ancestors' lockedDescendantCount
parent = node.parent
while parent:
parent.lockedDescendantCount += 1
parent = parent.parent

return True

def isAncestorLocked(self, node):
# Traverse up to check if any ancestor is locked
current = node.parent
while current:
if current.isLocked:
return True
current = current.parent
return False

def collectLockedDescendants(self, node, uid, locked_nodes):
# If there are no locked descendants, return True
if node.lockedDescendantCount == 0:
return True

# Check if current node is locked
if node.isLocked:
if node.uid == uid:
locked_nodes.append(node)
else:
# Locked by a different user
return False

# Recurse into children only if necessary
for child in node.children:
if child.lockedDescendantCount > 0:
if not self.collectLockedDescendants(child, uid, locked_nodes):
return False
return True

def process_queries(self):
results = []
for query in self.processed_queries:
operation, node_name, uid = query
node = self.node_map[node_name]
if operation == "1":
result = self.lock(node, uid)
elif operation == "2":
result = self.unlock(node, uid)
elif operation == "3":
result = self.upgrade(node, uid)
else:
result = False # Invalid operation
results.append('true' if result else 'false')
return results


def main():
n = int(sys.stdin.readline())
m = int(sys.stdin.readline())
q = int(sys.stdin.readline())

node_list = []
for _ in range(n):
node_list.append(sys.stdin.readline().strip())

queries = []
for _ in range(q):
queries.append(sys.stdin.readline().strip())

tree = Tree(n, m, node_list, queries)
results = tree.process_queries()
for res in results:
print(res)

main()