Practice Number theory and Arithmetic with the exercise "Numbers with only two distinct digits"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Number theory
Arithmetic
Mathematics

Statement

Goal

Given a strictly positive integer n and the two non 0 digits a and b (one is odd, the other is even), find the positive integer that has n digits (using only a or b) and that is divisible by 2^n .

There is always a unique integer satisfying all the conditions (you can try to prove it as an exercise).

Input

Line 1: A strictly positive integer n.
Line 2: Two digits a and b separated by a space.

Output

Line 1: The number you found

Constraints

0<n≤500
0<a, b<10
a and b have different parity.

Example

Input

1
2 5

Output

Solve it

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