Unfortunately, I have found out that the checker for problem E of Codeforces Educational Round 189 did not correctly verify the case when a circle does not cover any points. I am very sorry for this issue — I was not the person writing that checker, but proofreading it and fixing all of the bugs is my responsibility as the coordinator of the round, and I failed.
After discussing the issue with authors and analyzing the submissions, I have decided that dropping the constraint from the statement altogether, without any changes to verdicts during the round is the best course of action: the amount of changes in the scoreboard, compared to the situation if checker were working correctly, is negligible (perhaps even zero).
My reasoning for thisThere are two categories of people which might get affected by this decision:
people who have got Accepted without satisfying this condition. I believe (and this is corroborated by 10 random solutions I checked) that getting Accepted in this problem while ignoring this condition altogether is nigh-impossible because you cannot use more than $$$n$$$ circles, and if you pick $$$n$$$ circles with radii of $$$10^3$$$ in a rectangle of size $$$(2 \cdot 10^5) \times (2 \cdot 10^5)$$$, you still cover less than $$$80\%$$$ of the area, meaning that you cannot get Accepted by simply putting circles "randomly" without caring about the fact that they must cover points. Random solutions I've checked actually verify this condition, so I believe that the issue only affected a very small portion of people who got Accepted (I couldn't find even a single submission affected).
people who got WA on a later test. Not handling this condition means that you might pass more tests, but still won't pass the $$$36$$$-th test which actually forces you to choose circles covering the points. This means that some people got WA36 instead of WA2 which they should have received if the checker was correct, but it does not change their result overall.
This means that the issue with checker does not affect the round standings overall, hence I've decided to keep all the verdicts as they are.
The problem statement will be updated accordingly in about $$$10$$$ or $$$15$$$ minutes.
I once again would like to apologize for not checking everything enough times, and I hope the decision I've made ensures that the minimum possible number of people are affected by this bug in checker.
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