Problem D. Deadlock detector ≡

Statement

Resource sharing is an important problem in parallel programming. When parallel tasks must use common resource, such as input/output channel, they serialize their access by using locks.

Two basic locking primitives are provided:

• LOCK r — marks resource as locked by the calling task. If the resource is already locked by the same task, it does nothing. If it is locked by a different task, calling task is blocked (i.e. pauses execution and waits) until the resource is unlocked.
• UNLOCK r — unlocks given resource if it is locked by the current task, and does nothing otherwise.

After the execution of the last locking primitive of the task, all resources locked by that task are unlocked.

Locking guarantees that only a single task can access the resource at a time. However, carelessly written programs may still lead to some unfortunate situations. If task A has already locked resource P and tries to lock Q, while task B has already locked Q and tries to lock P, they will both wait endlessly. This condition is called "deadlock".

Your program must, given lock/unlock sequences executed by two parallel tasks while accessing M resources, determine whether a deadlock is possible between them.

Input file format

First line of input file contains integers N₁ N₂ M. Following lines contain N₁ locking primitives called by the first task, then N₂ primitives called by the second task, in the order of calling.

Each primitive is located on a separate line and consists of a string LOCK or UNLOCK followed by one or more spaces and a resource number r (1 ≤ r ≤ M).

Output file format

Output file must contain integers D₁ D₂, designating that deadlock can occur when the first task is trying to execute primitive number D₁ (1 ≤ D₁ ≤ N₁) while the second task is trying to execute primitive number D₂ (1 ≤ D₂ ≤ N₂).

If there is more than one possible deadlock, output the one with minimal D₁. If there is still more then one, output the one with minimal D₂. If the deadlock is not possible, output file must contain a single 0 (zero).

Constraints

Sample tests

2 2 2
LOCK 1
LOCK 2
LOCK 2
LOCK 1

2 2

3 3 5
LOCK 5
LOCK 2
LOCK 3
LOCK 5
LOCK 3
LOCK 2

0