Problem Statement

We have two sequences $A_1,\ldots, A_M$ and $B_1,\ldots,B_M$ consisting of intgers between 1 and N (inclusive).
For a string of length M consisting of 0 and 1, consider the following undirected graph with 2N vertices and (M+N) edges corresponding to that string.

• If the i-th character of the string is 0, the i-th edge connects Vertex A_i and Vertex (B_i+N).
• If the i-th character of the string is 1, the i-th edge connects Vertex B_i and Vertex (A_i+N).
• The (j+M)-th edge connects Vertex j and Vertex (j+N).

Here, i and j are integers such that $1 \leq i \leq M$ and $1 \leq j \leq N$,
and the vertices are numbered 1 to 2N.
Find one string of length M consisting of 0 and 1 such that the corresponding undirected graph has the minimum number of bridges.

Notes on bridges
A bridge is an edge of a graph whose removal increases the number of connected components.

Input

Input is given from Standard Input in the following format:
N M
$A_1 A_2 \cdots A_M$
$B_1 B_2 \cdots B_M$

Output

Print one string that satisfies the requirement. If there are multiple such strings, you may print any of them.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq N$

Sample Input 1

2 2
1 1
2 2

Sample Output 1

01

The graph corresponding to 01 has no bridges.
In the graph corresponding to 00, the edge connecting Vertex 1 and Vertex 3 and the edge connecting Vertex 2 and Vertex 4 are bridges, so 00 does not satisfy the requirement.

Sample Input 2

6 7
1 1 2 3 4 4 5
2 3 3 4 5 6 6

Sample Output 2

0100010

见题面 Input 部分

见题面 Output 部分