There are 10 agents living at their respective homes. They used a secret mailing system that sends one box at a time, but it is now spoilt. Now, it functions as follows:

* It counts the number of deliveries to each agent.
* It always sends the box to the agent with the lowest delivery count.
* If there is more than one such agent, it will pick one of them randomly.
* Once the box reaches an agent, it will remain there until that agent decides to send it.
* For security, the box will never travel unless there is a lock on it.
* The time taken by the distribution system to deliver a box is variable and random and always non-negligible, so waiting for a fixed number of seconds/minutes/days before sending a box is not a viable way of sending information. The transmission system creates a queue if it receives boxes while it already has a box in the process of being transmitted. Only one box can be in the process of transmission at one point in time, the rest are all on hold in the queue.

**Rules:**

* Each agent has an unlimited supply of boxes of various sizes, and padlocks (each with a single key). The padlocks look identical, the keys do not. This supply is given to them after the pre-planning phase.
* Any number of locked padlocks can be put on any box.
* A box can contain open/locked padlocks, keys, papers, and boxes, each with/without its own locks. (Note the difference between putting a padlock *on* a box, i.e., locking it, and putting a padlock *in* a box, i.e., transporting it)
* A padlock can be opened or closed only with its key.
* Boxes cannot change size. If Box A was once placed in Box B, Box B can not be placed in Box A ever.
* Keys and locks cannot be duplicated. Papers can be photocopied.
* The agents can have a pre-arranged plan, before they start the mission. Once the mission has started, they can communicate with each other only through papers (which they can create) that are sent in the box.
* The box used for delivery can be changed by an agent who opens it and can transfer the contents to a larger (or maybe even smaller) box. However, the mailing system will treat it just like the old one. The mailing order remains unchanged. The size of the new box will be random and hence its dimensions cannot convey information.
* pre-arranged planning only involves strategy talk, no handing out/exchanging locks or keys.
* no writings are to be made on the outside of the box sent around, nor messages taped to the side. No unlocked padlocks, etc. can be sticking out of the box.
* the lock(s) that is/are to be on the box when the message is sent, is/are required to be in locked state.
* the 'box transfer count' isn't visible, but held by the agency that does the box transportation.
* a person can send multiple boxes one after the other, but there should be negligible time lag between the transmissions.

**Mission**

Agent 001 has received a top secret message on a sheet of paper. He needs to inform all the agents. What is the minimum number of transmissions it will take before he can guarantee that everyone has received it (or a copy of it)?