You have been given formatted text and asked to converted it HTML.

Each character may be formatted as bold, italic, underlined, or some combination.

In HTML, content between <b> and </b> tags is bold. Content between <i> and </i> tags is italic. Content between <u> and </u> tags is underlined.

What is the minimum number of properly nested HTML tags needed to produce a given format?

For example, say we wanted to format <i><b>LookAt</b>Me</i>!

• <b><i>LookAt</b>Me</i>! has incorrectly nested tags.
• <b><i>LookAt</i></b><i>Me</i>! has correctly nested tags, but is longer than necessary.
• <i><b>LookAt</b>Me</i>! is the shortest and uses the fewest number of tags.

There will be a sequence of 1 to 20,000 numerals. Each numeral denotes the formatting at that position.

• 0 - no formatting
• 1 - bold
• 2 - italic
• 3 - bold and italic
• 4 - underlined
• 5 - bold and underlined
• 6 - italic and underlined
• 7 - bold, italic, and underlined

(There is no need to actually specify the content, since that will not affect the answer.)
The example earlier would be given as 333333220.

The minimum number of <b>, </b>, <i>, </i>, <u>, and </u> tags required.