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## 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

Your goal is to output the first

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

`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

1 ≤ A ≤ 9

1 ≤ B ≤ 9

A ≠ B

Example

Input

10 1 2

Output

1221121221

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