481. Magical String

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

• Concatenating the sequence of lengths of its consecutive groups of identical 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 counting the occurrences of 1's or 2's in each group yields the sequence "1 2 2 1 1 2 1 2 2 1 2 2 ......".

You can see that concatenating the occurrence sequence gives us 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:

• 1 <= n <= 105