Explore

Given a graph of n nodes numbered from 0 to n − 1, you need to find all m undirected edges through some operations.

Each node has a mark w, which is set to 0 initially. now you can apply 4 kinds of operations:

1. modify(x): For node x and all of x's direct neighbors, change each node's mark from w to w ⊕ 1 (⊕ denotes the exclusive or).

2. query(x): Return the current w value of node x.

3. report(x,y): Record that there is an edge between x and y.

4. check(x): Check if all edges incident on x have been reported.

For each operation, you can use them at most Lm, Lq, M, and Lc times, respectively.

Your job is to implement the function explore(N,M). N and M denote the number of nodes and edges respectively.

With the header explore.h, you can call these four functions:

1. modify(x): There will be no return value. Please make sure 0 ≤ x < N.

2. query(x): It will return the value w of node x. Please make sure 0 ≤ x < N.

3. report(x,y): It will record an edge between nodes x and y. Please make sure 0 ≤ x, y < N, x ≠ y.

4. check(x): It will return the status of node x. Please make sure 0 ≤ x < N. It will return 1 when all edges connected with x have been recorded. It will return 0 otherwise.

Note that all graphs are fixed in advance and won't change.

You can look at the units digit of N to distinguish the special graphs from the other cases.