Write overlapping text styles with the fewest tags

Your editor stores formatting as ranges over the text: bold from 3 to 9, italic from 5 to 12, and so on. To send a message as email, it writes HTML with <b>, <i>, <u> and <s> tags. Tags must nest properly, so a range that crosses another one has to be written as more than one tag. Email clients cut off long messages, so you want as few tags as possible.

Write fewest_tags(length, ranges) that returns the smallest number of elements the HTML needs.

Input and output:

• length: the number of characters in the text, from 0 to 100,000.
• ranges: up to 1,000 ranges, each [style, start, end]. style is "b", "i", "u" or "s". The range covers characters start to end - 1, where 0 <= start < end <= length. Ranges of the same style may overlap or touch.
• Returns an integer.

Rules:

• A character has a style when at least one range of that style covers it.
• An element is an opening tag, the characters inside it, and the matching closing tag. Each element has one style.
• Every character must be inside exactly one element of each style it has, and inside no element of a style it does not have.
• Elements nest properly: when 2 elements share a character, one of them lies entirely inside the other.
• Return the smallest number of elements that meets these rules.