Practice Coding with the exercise "Kolakoski Sequence"

Statement

Goal

A Kolakoski sequence, named after William Kolakoski, is an infinite sequence of digits whose run lengths reduce to the sequence itself.

For example, the Kolakoski sequence for the numbers 1 and 2 is
1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1…
because, when writing down the successive run lengths of 1s and 2s, you get the same sequence back:


Sequence:    1  2 2  1 1  2  1  2 2  1  2 2 …
             ↕   ↕    ↕   ↕  ↕   ↕   ↕   ↕
Run lengths: 1   2    2   1  1   2   1   2  …  ← same sequence

Your goal is to output the first N elements of the Kolakoski sequence given its first two distinct digits A and B.

Input

Line 1: The number N of digits to output
Line 2: The digits A and B which will form the sequence, in that order

Output

The Kolakoski sequence, without any separator.

Constraints

1 ≤ N ≤ 1000
1 ≤ A ≤ 9
1 ≤ B ≤ 9
A ≠ B

Example

Input

10
1 2

Output

1221121221

Solve it

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