Kanga directs her friends to march in a 3×3 grid. Each one wears a hat with an integer from 1 to 5 on it. They make the following statements. In these statements, "neighbor" includes diagonal adjacencies.

APRIL | Both my eastern neighbor and my southern neighbor have a 2 on their hats. |

BILLY | April and Freya are the only two people whose neighbors' numbers sum up to 15. |

COREY | The sum of my neighbors' numbers is 27, which is the highest possible neighbor sum. |

DAISY | There are exactly five people with the property that all their neighbors' hats have distinct numbers, but I am not one of them. |

ELSIE | The number on my hat is the floor of the average of all the numbers. |

FREYA | There is no one to my north. |

GOPAL | Four of my neighbors' hats have the same number. |

HOLLY | The sum of my neighbors' numbers is 7, which is the lowest possible neighbor sum. |

IZUMI | Holly is somewhere to my north. |