During a fight, each of the $2001$ roosters has torn out exactly one feather of another rooster, and each rooster has lost a feather. It turned out that among any three roosters there is one who hasn’t torn out a feather from any of the other two roosters. Find the smallest $k$ with the following property: It is always possible to kill $k$ roosters and place the rest into two henhouses in such a way that no two roosters, one of which has torn out a feather from the other one, stay in the same henhouse.