Given an integer ~X~, construct a string ~S~ ~(1 \leq |S| \leq 10^5)~ with only the characters a and b that has exactly ~X~ substrings that contain the character a.

If there are multiple solutions, you may print any.

Input Specification

The first and only line will contain an integer ~X\ (0 \leq X \leq 10^9)~.

Output Specification

You are to print one line, containing a string that satisfies the conditions outlined in the problem statement.

Note

It may be useful to know that the number of substrings of a string of length ~N~ is ~\frac{N(N+1)}{2}~.

Subtasks

Subtask 1 (80%)

~X \leq 55~

Subtask 2 (10%)

~X \leq 250~

Subtask 3 (10%)

No further constraints.

Sample Input 1

4

Sample Output 1

bab

Explanation for Sample 1

bab contains 6 substrings: b,a,b,ba,ab, and bab. 4 of these substrings contain the character a.

Sample Input 2

11

Sample Output 2

bbaba

Explanation for Sample 2

bbaba contains 15 substrings: b, b, a, b, a, bb, ba, ab, ba, bba, bab, aba, bbab, baba, bbaba. 11 of these substrings contain the character a.