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# [Thunno 2](https://github.com/Thunno/Thunno2), 14 bytes

```
6RẉDæḳ6R⁼;,ḷẸ\
```

[Attempt This Online!](https://ato.pxeger.com/run?1=m728JKM0Ly_faMGCpaUlaboWO82CHu7qdDm87OGOzWZBjxr3WOs83LH94a4dMUuKk5KLoaoWLDSDMAA)

Note: brute-force, so times out for \$n\ge5\$ on ATO, but I have verified it with \$n=6\$ on my computer.

#### Explanation

```python
6RẉDæḳ6R⁼;,ḷẸ\  # Implicit input
6R              # Push [1..6]
  ẉ             # Cartesian power with input
   D            # Duplicate the list
    æ    ;      # Filter by:
     ḳ          #  Sorted uniquify
      6R⁼       #  Exactly equal to [1..6]?
          ,     # Pair with original list
           ḷ    # Length of each list
            Ẹ   # Dump
             \  # Swapped divide
                # Implicit output
```