4's BFF in that input is 3, and in this circle: 4 1 3 2, 4 is not sitting next to 3, so the circle is not valid. We got a bunch of questions like this one during the contest. We check our samples carefully, both by hand and with programs written by different people independently, so if something seems odd, you should check that you are interpreting everything correctly, as that is most likely the case (we have a LOT more time to check the samples than you guys, and we are less nervous while doing so).
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