## --- Day 20: Infinite Elves and Infinite Houses ---

To keep the Elves busy, Santa has them deliver some presents by hand, door-to-door. He sends them down a street with infinite houses numbered sequentially: `1`

, `2`

, `3`

, `4`

, `5`

, and so on.

Each Elf is assigned a number, too, and delivers presents to houses based on that number:

- The first Elf (number
`1`

) delivers presents to every house:`1`

,`2`

,`3`

,`4`

,`5`

, .... - The second Elf (number
`2`

) delivers presents to every second house:`2`

,`4`

,`6`

,`8`

,`10`

, .... - Elf number
`3`

delivers presents to every third house:`3`

,`6`

,`9`

,`12`

,`15`

, ....

There are infinitely many Elves, numbered starting with `1`

. Each Elf delivers presents equal to *ten times* his or her number at each house.

So, the first nine houses on the street end up like this:

```
House 1 got 10 presents.
House 2 got 30 presents.
House 3 got 40 presents.
House 4 got 70 presents.
House 5 got 60 presents.
House 6 got 120 presents.
House 7 got 80 presents.
House 8 got 150 presents.
House 9 got 130 presents.
```

The first house gets `10`

presents: it is visited only by Elf `1`

, which delivers `1 * 10 = 10`

presents. The fourth house gets `70`

presents, because it is visited by Elves `1`

, `2`

, and `4`

, for a total of `10 + 20 + 40 = 70`

presents.

What is the *lowest house number* of the house to get at least as many presents as the number in your puzzle input?