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Like every IT company, the Uplink Corporation has its own network. But, unlike the rest of the companies around the world, Uplink's network is subject to very specific restrictions:

• Any pair of servers within the network should be directly connected by at most 1 link.
• Each link is controlled by some specific network administrator.
• No server has more than 2 links connected to it, that are controlled by the same administrator.
• For easier management, links controlled by some administrator cannot be redundant (this is, removing any link will disconnect some two previously connected servers)

Notice that 2 connected servers might not have any direct link between them. Furthermore, in order to keep the network in a secured status, Uplink directives periodically try to perform some modifications over the network to mislead hackers. The problem is, having such a huge network, they need a software to efficiently simulate the network status after any of such modifications. You have been assigned to write the core section of that software.

Operations performed by the directives are:

• Change the administrator assigned to some particular link.
• Place some number of security devices along a particular link.

Also, given a network administrator, they would like to know how many devices are in the path created by links controlled by that administrator (if any) between 2 servers.

Input Format
Input begins with a line containing 4 integers separated by a single whitespace, denoting the number of servers, links, network administrators and transformations, respectively. lines follow each one with 3 integers and , saying that there is a link between server and server , and that link is controlled by administrator . Initially, network topology fulfills the restrictions described above and there is no security device along any link. Remaining lines in the input follow one the next formats:

meaning that link between server and server is requested to be assigned to administrator

meaning that the number of security devices along the link between server and server will be fixed to , removing any existing devices on this link before the operation. The involved link will always exist.

meaning that directives want to know the number of security devices placed along the path between server and server , just considering links controlled by administrator .

Output Format
For each network transformation in the form you should output:

• "Wrong link" if there is no direct link between server and server .
• "Already controlled link" if the requested link does exist, but it is already controlled by administrator .
• "Server overload" if administrator already controls 2 links connected to one of the involved servers.
• "Network redundancy" if the requested assignment creates no new connection considering just the links controlled by .
• "Assignment done" if none of the above conditions holds. In this case, link directly connecting with is assigned to .

For each network transformation in the form you should output:

• "No connection" if there is no path between the requested servers considering just the links controlled by .
• " security devices placed" where D is the number of security devices placed so far on the existing connection between the requested servers considering just the links controlled by .

Constraints

Sample Input:

4 5 3 15
1 2 1
2 3 1
3 4 2
1 4 2
1 3 3
2 3 4 49
1 1 2 3
2 1 4 64
3 1 4 2
1 1 2 3
3 4 2 3
3 1 3 3
1 1 4 3
3 3 4 2
3 2 4 1
2 1 4 13
2 1 3 21
2 2 3 24
1 2 3 3
1 2 4 3

Sample Output:

Assignment done
64 security devices placed
Already controlled link
No connection
0 security devices placed
Server overload
49 security devices placed
No connection
Network redundancy
Wrong link