There are 2026 people at a big party. Starting one minute after midnight, the host begins sending people home in a strange way.
After 1 minute, anyone with no friends at the party leaves. After 2 minutes, anyone with exactly one friend left in the party leaves. After 3 minutes, anyone with exactly two friends left leaves, and so on.
Show that there will always be at least two people who have left at some point the party after \(2026\) minutes have passed.