Domain clusters

We analyze how the domains on the Internet link to each other. A domain is the part of a URL that comes before the / character. twitter.com, aipo.computing.dcu.ie, and google.com are domains.

A domain d1 is connected to a domain d2 if there is a link from d1 to d2, or if d1 is connected to a domain d3 and d3 is connected to d2. Every domain is connected to itself.

The picture below shows a structure of five domains. Its links go from D1 to D2, D1 to D4, D2 to D3, D3 to D2, D3 to D4, D3 to D5, and D5 to D2.

• D1 is connected to D2, D3 (through D2), D4, and D5 (through D3).
• D2 is connected to D3, D4 (through D3), and D5 (through D3).
• D3 is connected to D2, D4, and D5.
• D4 is not connected to any other domain.
• D5 is connected to D2, D3 (through D2), and D4 (through D3).

We want the largest set of domains $S$ in which every domain is connected to all the other domains of $S$. In the structure above the sets that meet this criterion are:

• {D1}: connected to itself.
• {D2, D3, D5}: D2 reaches D3 and D5, D3 reaches D2 and D5, and D5 reaches D2 and D3.
• {D4}: connected to itself.

Given the links of the Internet, compute the size of the largest such set.

The first line contains an integer $D$, the number of domains. The names of the domains are the integers from $1$ to $D$. ($1 \le D \le 5000$)

The second line contains an integer $L$, the number of links between domains. Each of the following $L$ lines contains two integers. The first integer is the source of the link and the second is the destination. A link from A to B does not imply a link from B to A, and every domain is connected to itself without an explicit link. No link appears more than once. ($0 \le L \le D^2$)

Print the size of the largest set of domains that meets the criterion above. If two or more sets tie for the largest size, print that size once.