Ransom

This is an interactive problem.

After Baldr was killed, Odin decided to bring him back to Asgard from Helheim, the realm of the dead. He gave his horse Sleipnir to Hermod and sent him to Hel, the goddess of the dead, to offer a ransom for Baldr. Hel agreed to release him if everything in the world, all things and creatures, wept for Baldr. That demand could not be met, so Hermod and Hel began discussing other ransom amounts.

Hermod said the world has $n$ cities, and every person living in them is ready to mourn Baldr. Let $a_i$ be the population of city $i$. He refused to name the population of any city. He agreed to answer a few questions instead, each of the form: tell me the product $a_{i_1} \times a_{i_2} \times \ldots \times a_{i_k}$, where $i_1, \ldots, i_k$ are distinct indices of some of these cities. He allowed at most $n$ questions.

Help the ruler of the dead find how many people live in each city.

The number the judge returns after each query can be quite large.

For the program to work correctly, you must do the following after every output operation:

• Pascal: flush(output);
• C/C++: fflush(stdout);
• Java: System.out.flush();
• Python: sys.stdout.flush();

Also end every printed line with a newline character.