Magical String
A magical string s consists only of '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 stringsitself.
The first few elements of s are 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 numbers in the magical string s.
Example 1
Input
n = 6Output
3The first 6 elements of magical string s are "122112" and it contains three 1's, so return 3.
Example 2
Input
n = 1Output
1The first element of the magical string is "1", so it contains one 1.
Constraints
- 1 <= n <= 10^5
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