package main

import (
	"cmp"
	"slices"
)

type Factor struct {
	factor int
	index  int
	next   int
}

func MakeFactor(factor int) Factor {
	return Factor{
		factor: factor,
		index:  0,
		next:   factor,
	}
}

func (f *Factor) Update(ugly []int, last int) {
	if last != f.next {
		return
	}

	f.index++
	f.next = f.factor * ugly[f.index]
}

func nthUglyNumber(n int) int {
	ugly := make([]int, n)
	ugly[0] = 1

	factors := []Factor{
		MakeFactor(2), MakeFactor(3), MakeFactor(5),
	}

	for i := 1; i < n; i++ {
		ugly[i] = slices.MinFunc(factors, func(a, b Factor) int {
			return cmp.Compare(a.next, b.next)
		}).next

		for j, _ := range factors {
			factors[j].Update(ugly, ugly[i])
		}
	}

	return ugly[n-1]
}