use binary heap with a type that doesn't implement Ord?

I'm creating a cli board game and I'm writing a simple minimax to play the game. Before evaluating the moves possible from a position, I want to sort them from best to worst and I thought to use a binary heap instead of pushing everything into a vector and then sort it.

1. Is there a struct in std like BinaryHeap<T> where T doesn't have to implement ord and instead you assign each value a "priority value"?
2. Is there a general struct in std that represents value with priority?:

​

struct Prioritized<T> {
    priority: u32,
    value: T
}

impl<T> PartialEq for Prioritized<T> {
    fn eq(&self, other: &Self) -> bool {
        self.priority.eq(&other.priority)
    }
}

impl<T> Eq for Prioritized<T> {}

impl<T> PartialOrd for Prioritized<T> {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        self.priority.partial_cmp(&other.priority)
    }
}

impl<T> Ord for Prioritized<T> {
    fn cmp(&self, other: &Self) -> Ordering {
        self.priority.cmp(&other.priority)
    }
}