481\. Magical String

Medium

A magical string `s` consists of only `'1'` and `'2'` and obeys the following rules:

*   The string s is magical because concatenating the number of contiguous occurrences of characters `'1'` and `'2'` generates the string `s` itself.

The first few elements of `s` is `s = "1221121221221121122……"`. If we group the consecutive `1`'s and `2`'s in `s`, it will be `"1 22 11 2 1 22 1 22 11 2 11 22 ......"` and the occurrences of `1`'s or `2`'s in each group are `"1 2 2 1 1 2 1 2 2 1 2 2 ......"`. You can see that the occurrence sequence is `s` itself.

Given an integer `n`, return the number of `1`'s in the first `n` number in the magical string `s`.

**Example 1:**

**Input:** n = 6

**Output:** 3

**Explanation:** The first 6 elements of magical string s is "122112" and it contains three 1's, so return 3.

**Example 2:**

**Input:** n = 1

**Output:** 1

**Constraints:**

*   <code>1 <= n <= 10<sup>5</sup></code>