Pottery Lottery

The Pottery Palace is going to run a lottery featuring some valuable vases by the artist Cody-Jamal. The lottery works as follows:

• 100 people get to play in the lottery. Each player has a unique number between 1 and 100, and is given a single token with that number.
• There are 20 empty clay vases on a table, numbered 1 through 20. The vases have narrow openings that are large enough to accept a token, but small enough that players cannot look inside to see the contents.
• On the i-th day of the lottery, the player with token number i chooses a vase and puts their token in that vase. Since the vases are all identical (apart from their labels), every player will choose one uniformly at random and independently of all other players' choices.
• On day 100, after player number 100 has inserted their token, the organizers shake the vases to determine how many tokens are inside each one. If there is exactly one vase that has fewer tokens than any other vase, then that one is the "winning vase". The organizers then pour out all of the tokens in that vase, and every player whose number is written on one of those poured-out tokens wins a vase! If multiple vases have the same minimal amount of tokens, nobody wins anything.

You have been hired to test the security of the lottery, and you will participate in some trial runs. The company will always assign you the number 100 — that is, you replace player 100.

You have found some ways to tamper with the lottery at night, but security is tight, so you can only do so much! Specifically, after each of the first 99 days of the lottery, you may do exactly one of the following:

• forge a token with the player number of your choice (between 1 and 100, inclusive), and add it to a vase of your choice. You are a very good forger: if there is a winning vase, any forged tokens in that vase will cause the players with those numbers to win (with one exception; see below).
• use a special camera to see the numbers on all of the tokens in one vase of your choice

You may perform different actions on different nights, and you may choose dynamically: you do not need to decide on all of your actions in advance.

On the 100th day, it is your turn to insert your token into a vase of your choice (you do not need to choose uniformly at random). You cannot perform any other actions on that day.

You know that if there is a winning vase with more than one token for the same player, it will be obvious that cheating has occurred and nobody will win. However, it does not matter if other vases contain more than one token for the same player because the organizers never see those tokens.

Your goal is to be a winner in at least 90% of the test cases.