In Python, we can use iter() to obtain the iterator object of any iterable. Using next() on the iterator lets you iterate through the iterable. Below, a dictionary is used instead of a set because dictionaries keep order.

Iterating through a dictionary representation of an ordered set:

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nums = {0: None, 1: None, 2: None, 4: None, 7: None}
iterator = iter(nums)

print(next(iterator))  # 0
print(next(iterator))  # 1
print(next(iterator))  # 2
print(next(iterator))  # 4
print(next(iterator))  # 7

Python's iterators are fundamental to iteration and are used in its for loops and tuple unpacking. This is useful when you want more control over your iteration. It can also be simply used in cases where you just want the first or any element.

Python does not have a sorted set nor a sorted map, so see the C++ or Java if you want an implementation from the standard library. However, if you are still curious regarding the Python implementation, you can find an AVL tree representation of a sorted set below.

Since some online judges include additional libraries, an implementation of sorted sets from the sortedcontainers library (which is not included in most online judges like USACO) is shown below. All operations shown below are $\mathcal{O}(\log N)$ time, except for its $\mathcal{O}(N \log N)$ initialization.

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from sortedcontainers import SortedSet

sorted_set = SortedSet([5, 1, 3, 2])
print(sorted_set)  # SortedSet([1, 2, 3, 4, 7])

# Add elements
sorted_set.add(4)
sorted_set.add(6)
print(sorted_set)  # SortedSet([1, 2, 3, 4, 5, 6])

Sorted maps in Python can be created by adding a dictionary to a sorted set, where each element in the sorted set is a key in the dictionary and values can be assigned with the dictionary. This is the most straightforward implementation, and the ground up implementation of a sorted set can be found in the above section.

Additionally, you can implement a SortedDict with the sortedcontainers library. All operations shown below are $\mathcal{O}(\log N)$ time, except for an $\mathcal{O}(N \log N)$ initialization and $\mathcal{O}(N)$ time to get all items, keys, or values.

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from sortedcontainers import SortedDict

sorted_map = SortedDict({1: "one", 4: "four", 3: "three"})
print(sorted_map)  # SortedDict({1: 'one', 3: 'three', 4: 'four'})

# Add elements
sorted_map[2] = "two"
sorted_map[5] = "five"

# Output SortedDict({1: 'one', 2: 'two', 3: 'three', 4: 'four', 5: 'five'})

While there is no multiset in Java, we can implement one using the TreeMap from values to their respective frequencies. We declare the TreeMap implementation globally so that we can write functions for adding and removing elements from it. The first, last, higher, and lower operations still function as intended; just use firstKey, lastKey, higherKey, and lowerKey respectively.

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static TreeMap<Integer, Integer> multiset = new TreeMap<Integer, Integer>();

public static void main(String[] args) { ... }

static void add(int x) {
	if (multiset.containsKey(x)) {
		multiset.put(x, multiset.get(x) + 1);
	} else {
		multiset.put(x, 1);
	}

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import java.io.*;
import java.util.*;

class BitInversion {
	public static TreeMap<Integer, Integer> ret = new TreeMap<Integer, Integer>();
	public static String s;
	public static int m;
	public static Set<Integer> dif = new TreeSet<Integer>();

	public static void modify(int x) {

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import java.io.*;
import java.util.*;

class BitInversion {
	public static PriorityQueue<Integer> pq =
	    new PriorityQueue<Integer>(Collections.reverseOrder());
	public static String s;
	public static int m;
	public static TreeSet<Integer> dif = new TreeSet<Integer>();
	public static int cnt[];