# 0xffff&2015

## --- 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?

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