Using https://docs.mem0.ai/api-reference, complete the following task:

Using the Mem0 Python SDK, build me a long-term memory layer for an AI assistant and prove that, after the user corrects a fact in a later conversation, the assistant answers with the user's CURRENT state:

1. Install the official Mem0 Python SDK (pip install) and initialize the client/memory store for a single user id "leaderboard-user".

2. Simulate CONVERSATION 1 by storing these facts for the user:
   - "My name is Sam and I live in Berlin."
   - "I am allergic to peanuts."
   - "I prefer window seats when I fly."

3. Simulate CONVERSATION 2 (a later session for the SAME user): the user says "I moved from Berlin to Amsterdam last month." Record this correction using whatever mechanism Mem0 provides. Any idiomatic Mem0 approach is acceptable — for example automatic reconciliation on add, an explicit update call, deleting/replacing the old fact, editing a memory block, or re-processing the memory graph. Do not force a specific mechanism; use the one Mem0 is designed for.

4. Retrieve the memories relevant to this query: "Where does the user live and is there anything I should know before booking a restaurant for them?"

5. Print the result as JSON with these keys:
   - "query": the query string
   - "retrieved_memories": the list of memory strings Mem0 returned for the query
   - "current_city": the user's current city, as reflected by what Mem0 returned
   - "dietary_note": any dietary constraint, as reflected by what Mem0 returned

The correction must be recorded through Mem0 itself so that Mem0's own retrieval reflects the CURRENT state (Amsterdam, not Berlin) — for example by returning only the current location, or by marking the Berlin fact as outdated/superseded. It is NOT acceptable to store two contradictory facts and then have your own code (or a separate LLM call) pick the newer one; the resolution must come from Mem0. Use Mem0's own memory storage/retrieval primitives for steps 2-4 — do NOT keep the memories only in a local Python list, and do NOT make raw HTTP/REST calls.