Amusement Park Adventure

You are given an undirected graph representing an amusement park. The park consists of n rooms (numbered from 1 to n) and m bidirectional passages connecting them. One of these rooms is designated as the central room, labeled with index c. Your task is to determine:

• The total number of rooms accessible from the central room.
• The minimum number of passages needed to reach each room from the central room. For rooms that are not accessible, output -1.

You may use the Breadth-First Search (BFS) algorithm. In mathematical terms, if the distance from room c to some room i is d(i), then for every passage \( (u,v) \) used in the shortest path we have \( d(v) = d(u) + 1 \). Print the results as described below.

inputFormat

The input is given via standard input (stdin) in the following format:

n m c
u1 v1
u2 v2
... 
um vm

Here, n is the number of rooms, m is the number of passages, and c is the index of the central room. Each of the next m lines contains two integers u and v indicating that there is a passage between room u and room v.

outputFormat

The output should be printed to standard output (stdout) in two lines:

1. The first line contains a single integer: the number of rooms accessible from the central room.
2. The second line contains n space-separated integers, where the i-th integer represents the minimum number of passages needed to reach room i from the central room. If a room is not accessible, output -1 for that room.

## sample

5 4 1
1 2
2 3
3 4
4 5

5
0 1 2 3 4

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