A magical stringSconsists of only '1' and '2' and obeys the following rules:

The stringSis magical because concatenating the number of contiguous occurrences of characters '1' and '2' generates the stringSitself.

The first few elements of stringSis the following:S= "1221121221221121122……"

If we group the consecutive '1's and '2's inS, 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 above is theSitself.

Given an integer N as input, return the number of '1's in the first N number in the magical stringS.

Note:N will not exceed 100,000.

Example 1:

Input:
 6

Output:
 3

Explanation:
 The first 6 elements of magical string S is "12211" and it contains three 1's, so return 3.

class Solution {
    public int magicalString(int n) {
        if (n == 0) return 0;
        if (n <= 3) return 1;

        int[] num = new int[n + 1];
        num[0] = 1; num[1] = 2; num[2] = 2;
        int head = 2, tail = 3;
        int flag = 1, count = 1;

        while (tail < n){
            for (int i = 0; i < num[head]; i++){
                num[tail] = flag;
                if (flag == 1 && tail < n) count++;
                tail++;
            }

            flag ^= 3;
            head++;
        }

        return count;
    }
}