---
id: 5900f4481000cf542c50ff5a
challengeType: 5
title: 'Problem 219: Skew-cost coding'
---
## Description
Let A and B be bit strings (sequences of 0's and 1's).
If A is equal to the leftmost length(A) bits of B, then A is said to be a prefix of B.
For example, 00110 is a prefix of 001101001, but not of 00111 or 100110.
A prefix-free code of size n is a collection of n distinct bit strings such that no string is a prefix of any other. For example, this is a prefix-free code of size 6:
0000, 0001, 001, 01, 10, 11
Now suppose that it costs one penny to transmit a '0' bit, but four pence to transmit a '1'.
Then the total cost of the prefix-free code shown above is 35 pence, which happens to be the cheapest possible for the skewed pricing scheme in question.
In short, we write Cost(6) = 35.
What is Cost(109) ?
## Instructions
## Tests
```yml
tests:
- text: euler219() should return 64564225042.
testString: 'assert.strictEqual(euler219(), 64564225042, "euler219() should return 64564225042.");'
```
## Challenge Seed
```js
function euler219() {
// Good luck!
return true;
}
euler219();
```