import java.util.HashMap;

class AllOne {
  private class Node {
    int freq;
    Node prev, next;
    Set<String> keys = new HashSet<>();

    Node(int freq) {
      this.freq = freq;
    }

    Node(int freq, Node prev, Node next) {
      this.freq = freq;

      this.prev = prev;
      prev.next = this;

      this.next = next;
      next.prev = this;
    }

    void link(Map<String, Node> map, String key) {
      keys.add(key);
      map.put(key, this);
    }

    void remove() {
      var prev = this.prev;
      var next = this.next;

      prev.next = next;
      next.prev = prev;
    }
  }

  Node head, tail;
  Map<String, Node> map = new HashMap<>();

  public AllOne() {
    head = new Node(0);
    tail = new Node(0);

    head.next = tail;
    tail.prev = head;
  }

  public void inc(String key) {
    if (!map.containsKey(key)) {
      var first = head.next;
      if (first != tail && first.freq <= 1) {
        first.link(map, key);
        return;
      }

      var newNode = new Node(1, head, first);
      newNode.link(map, key);
      return;
    }

    var node = map.get(key);
    var freq = node.freq;
    node.keys.remove(key);

    var next = node.next;
    if (next != tail && next.freq == freq + 1) {
      next.link(map, key);
    } else {
      var newNode = new Node(freq + 1, node, next);
      newNode.link(map, key);
    }

    if (node.keys.isEmpty()) {
      node.remove();
    }
  }

  public void dec(String key) {
    if (!map.containsKey(key)) {
      return;
    }

    var node = map.get(key);
    var freq = node.freq;
    node.keys.remove(key);

    if (freq == 1) {
      map.remove(key);
    } else {
      var prev = node.prev;
      if (prev != head && prev.freq == freq - 1) {
        prev.link(map, key);
      } else {
        var newNode = new Node(freq - 1, prev, node);
        newNode.link(map, key);
      }
    }

    if (node.keys.isEmpty()) {
      node.remove();
    }
  }

  public String getMaxKey() {
    if (tail.prev == head) {
      return "";
    }

    return tail.prev.keys.iterator().next();
  }

  public String getMinKey() {
    if (head.next == tail) {
      return "";
    }

    return head.next.keys.iterator().next();
  }
}