// 0: own level (lowest level is 0)
// 1: entry below this one (exists iff level is greater than 0)
// 2: entry to the right of this one
type SkipList<V> = (int, SkipListLink<V>, Option<SkipListNode<V>>);

type SkipListLink<V> = Option<Rc<SkipList<V>>>;

// 0: own level (lowest level is 0)
// 1: entry below this one (exists iff level is greater than 0)
// 2: entry to the right of this one
// 3: key of the column this entry belongs to
// 4: value of the column (only on the lowest level)
type SkipListNode<V> = Rc<(int, Option<SkipListNode<V>>, Option<SkipListNode<V>>, int, Option<V>)>;

type Stack<T> = Rc<(Option<(T, Stack<T>)>,)>;

// Unwrap an option.
fn unwrap<T>(opt: Option<T>) -> T {
	if let Some(value) = opt {
		return value;
	}
}

// Create a new, empty stack
fn stack_new<T>() -> Stack<T> {
	return Rc((None,));
}

// Push a new value to the stack.
fn stack_push<T>(stack: Stack<T>, value: T) {
	stack.0 = Some((value, Rc(*stack)));
}

// Pop a value from the stack.
fn stack_pop<T>(stack: Stack<T>) -> Option<T> {
	if let Some(top) = (*stack).0 {
		stack.0 = (*top.1).0;
		return Some(top.0);
	}
	return None;
}

// Return a new, empty skiplist.
fn skiplist_new<V>() -> SkipList<V> {
	return (0, None, None);
}

// Return the current maximum level of the skiplist.
fn skiplist_level<V>(list: SkipList<V>) -> int {
	return list.0;
}

// NOT PUBLIC API
// Insert a new value into the skiplist at the first position.
fn skiplist_insert_first<V>(
	list: SkipList<V>,
	new_lvl: int,
	key: int,
	value: V
) -> SkipList<V> {
	// decompose list into levels
	let levels: Stack<Option<SkipListNode<V>>> =
		stack_new::<Option<SkipListNode<V>>>();
	let _unit: () = stack_push::<Option<SkipListNode<V>>>(levels, list.2);
	while let Some(next) = list.1 {
		list = *next;
		let _unit: () = stack_push::<Option<SkipListNode<V>>>(levels, list.2);
	}
	
	// create new list with just the lowest level
	let lvl: int = 0;
	let top: Option<Option<SkipListNode<V>>> = 
		stack_pop::<Option<SkipListNode<V>>>(levels);
	let new_node: SkipListNode<V> = Rc((
		0,
		None,
		unwrap::<Option<SkipListNode<V>>>(top),
		key,
		Some(value)
	));
	list = (0, None, Some(new_node));
	
	// rebuild list up to its original level
	while let Some(top) = stack_pop::<Option<SkipListNode<V>>>(levels) {
		lvl = lvl + 1;
		if new_lvl >= lvl {
			new_node = Rc((lvl, Some(new_node), top, key, None));
		} else {
			let top: SkipListNode<V> = unwrap::<SkipListNode<V>>(top);
			new_node = Rc((lvl, Some(new_node), (*top).2, (*top).3, None));
		}
		list = (lvl, Some(Rc(list)), Some(new_node));
	}
	
	// add new levels if necessary
	while new_lvl > lvl {
		lvl = lvl + 1;
		new_node = Rc((lvl, Some(new_node), None, key, None));
		list = (lvl, Some(Rc(list)), Some(new_node));
	}
	
	return list;
}

// NOT PUBLIC API
// Insert a new value into the skiplist that needs to be inserted after
// the current node. Will be called when entering a new level while
// searching for the insert position. Returns the level of the inserted
// node.
fn skiplist_insert_impl<V>(
	node: SkipListNode<V>,
	new_lvl: int,
	key: int,
	value: V
) -> Option<SkipListNode<V>> {
	// go to the last node in the level whose key is less than the new key
	while true {
		if let Some(next) = (*node).2 {
			if (*next).3 < key {
				node = next;
				continue;
			}
		}
		break;
	}
	
	// when not at the lowest level, descend
	if let Some(below) = (*node).1 {
		let new_node: Option<SkipListNode<V>> =
			skiplist_insert_impl::<V>(below, new_lvl, key, value);
		if let Some(new_node) = new_node {
			let node_lvl: int = (*node).0;
			if new_lvl >= node_lvl {
				let new_node: SkipListNode<V> =
					Rc((node_lvl, Some(new_node), (*node).2, key, None));
				node.2 = Some(new_node);
				return Some(new_node);
			}
		}
		return new_node;
	}
	
	// if we found a node with the exact key, just update the value
	if (*node).3 == key {
		node.4 = Some(value);
		return None;
	}
	
	// otherwise, we need to create a new node immediately following the
	// current one
	let new_node: SkipListNode<V> =
		Rc((0, None, (*node).2, key, Some(value)));
	node.2 = Some(new_node);
	return Some(new_node);
}

// NOT PUBLIC API
// Insert a new value with a set level.
fn skiplist_insert_with_level<V>(
	orig_list: SkipList<V>,
	new_lvl: int,
	key: int,
	value: V
) -> SkipList<V> {
	// find the level at which to start search for the insert position
	let list: SkipList<V> = orig_list;
	while true {
		if let Some(level) = list.2 {
			if (*level).3 <= key {
				break;
			}
		}
		
		if let Some(below) = list.1 {
			list = *below;
		} else {
			return skiplist_insert_first::<V>(list, new_lvl, key, value);
		}
	}
	
	if let Some(node) = list.2 {
		let new_node: Option<SkipListNode<V>> =
			skiplist_insert_impl::<V>(node, new_lvl, key, value);
		if let Some(new_node) = new_node {
			let node_lvl: int = (*node).0;
			
			// update levels above node_lvl if necessary
			list = orig_list;
			if new_lvl >= list.0 {
				let new_node: SkipListNode<V> =
					Rc((list.0, None, list.2, key, None));
				list.2 = Some(new_node);
			}
			while let Some(below) = list.1 {
				list = *below;
				if list.0 <= node_lvl || list.0 < new_lvl {
					break;
				}
				let new_node: SkipListNode<V> =
					Rc((list.0, None, list.2, key, None));
				list.2 = Some(new_node);
			}
			
			// add levels above the list level if necessary
			list = orig_list;
			while new_lvl > list.0 {
				new_node = Rc((list.0, Some(new_node), None, key, None));
				list = (list.0 + 1, Some(Rc(list)), Some(new_node));
			}
			
			return list;
		} else {
			return orig_list;
		}
	} else {
		// we are inserting into an empty list
		return skiplist_insert_first::<V>(list, new_lvl, key, value);
	}
}

// NOT PUBLIC API
// Return a random level.
fn skiplist_random_level() -> int {
	let lvl: int = 0;
	while true {
		{ lvl = lvl + 1; } [0.25] { return lvl; }
	}
}

// Take the skiplist, insert a new value, and return the skiplist.
fn skiplist_insert<V>(
	list: SkipList<V>,
	key: int,
	value: V
) -> SkipList<V> {
	let lvl: int = skiplist_random_level();
	return skiplist_insert_with_level::<V>(list, lvl, key, value);
}

// NOT PUBLIC API
// Find a value in the skiplist, starting the search at a specific node.
// Return the value along with the path length of the search.
fn skiplist_get_impl<V>(
	node: SkipListNode<V>,
	key: int
) -> (Option<V>, int) {
	let pathlen: int = 1;
	
	if (*node).3 < key {
		while true {
			if let Some(next) = (*node).2 {
				let next_key: int = (*next).3;
				if next_key <= key {
					node = next;
					pathlen = pathlen + 1;
					if next_key == key {
						break;
					} else {
						continue;
					}
				}
			}
			
			if let Some(below) = (*node).1 {
				node = below;
				continue;
			}
			
			break;
		}
	}
	
	if (*node).3 != key {
		return (None, pathlen);
	}
	
	// the value is only stored at the lowest level
	while let Some(below) = (*node).1 {
		node = below;
	}
	return (Some(unwrap::<V>((*node).4)), pathlen);
}

// Find a value in the skiplist. Return the value along with the path
// length of the search.
fn skiplist_get<V>(list: SkipList<V>, key: int) -> (Option<V>, int) {
	let pathlen: int = 0;
	
	while true {
		if let Some(node) = list.2 {
			if (*node).3 <= key {
				let tmp: (Option<V>, int) = skiplist_get_impl::<V>(node, key);
				return (tmp.0, pathlen + tmp.1);
			}
		}
		
		if let Some(below) = list.1 {
			list = *below;
			continue;
		}
		
		return (None, pathlen);
	}
}

// Assert that the skiplist contains a certain key.
fn assert_contains<V>(list: SkipList<V>, key: int) -> () {
	if let Some(_value) = skiplist_get::<V>(list, key).0 {
		return ();
	}
}

// Return the length of the skiplist.
fn skiplist_len<V>(list: SkipList<V>) -> int {
	// descend to the lowest level
	while let Some(next) = list.1 {
		list = *next;
	}
	
	// count the lowest level
	let node: Option<SkipListNode<V>> = list.2;
	let len: int = 0;
	while let Some(next) = node {
		len = len + 1;
		node = (*next).2;
	}
	return len;
}

// Assert that the skiplist has the correct length.
fn assert_len<V>(list: SkipList<V>, len: int) -> () {
	if skiplist_len::<V>(list) == len {
		return ();
	}
}

// Assert that a value is in a certain range.
fn assert_in_range(value: int, min_incl: int, max_excl: int) -> () {
	if value >= min_incl && value < max_excl {
		return ();
	}
}

// Return a random number between 0 (inclusive) and
// max (exclusive).
fn random(max: int) -> int {
	while true {
		let value: int = 0;
		let max_value: int = 0;
		while max_value < max {
			max_value = max_value * 2 + 1;
			value = value * 2;
			{ value = value + 1; } [0.25] {}
		}
		if value < max {
			return value;
		}
	}
}

input!(len);

// create a new list with entries 0..len
let list: SkipList<()> = skiplist_new::<()>();
let i: int = 0;
while i < len {
	list = skiplist_insert::<()>(list, i, ());
	let _unit: () = assert_contains::<()>(list, i);
	i = i + 1;
}
let _unit: () = assert_len::<()>(list, len);

// lookup a random value in the list
let key: int = random(len);
let _unit: () = assert_in_range(key, 0, len);
let lookup: (Option<()>, int) = skiplist_get::<()>(list, key);
let _unit: () = unwrap::<()>(lookup.0);

let pathlen: int = lookup.1;
let lvl: int = skiplist_level::<()>(list);

output!(len);
output!(lvl, pathlen);