Given $N, K, L$, construct two binary strings $S$ and $T$ such that:

• Both $S$ and $T$ have length $N$.
• $S$ contains exactly $K$ ones.
• $T$ contains exactly $L$ ones.

Subject to these conditions, you want to minimize:

• The maximum number of ones in the binary string $R_i$ where $R_i = S_i \operatorname{and} T_i$, after applying any cyclic shift to $S$ and $T$.

Input

The input consists of a single line containing three integers $N, K, L$. It is guaranteed that $0 \leq K, L \leq N$.

Output

The first line of the output contains an integer representing the minimum value for the optimal construction.

The next line describes the constructed string $S$.

The next line describes the constructed string $T$.

If there are multiple valid solutions, you may output any one of them.

Examples

Input 1

6 4 3

Output 1

2
011011
101010

Input 2

5 2 0

Output 2

0
01001
00000

Input 3

10 7 6

Output 3

5
1101100111
1110001101

Subtasks

Specifically, if your program outputs the correct result on the first line but the constructed solution is incorrect, you can receive $20\%$ of the points for that test case.