Problem Description

Suppose that G is an undirected graph, and the value of stab is defined as follows:

Among the expression,G_{-i, -j} is the remainder after removing node i, node j and all edges that are directly relevant to the previous two nodes. cntCompent is the number of connected components of X independently.
Thus, given a certain undirected graph G, you are supposed to calculating the value of stab.

 

Input

The input will contain the description of several graphs. For each graph, the description consist of an integer N for the number of nodes, an integer M for the number of edges, and M pairs of integers for edges (3<=N,M<=5000).
Please note that the endpoints of edge is marked in the range of [0,N-1], and input cases ends with EOF.

 

Output

For each graph in the input, you should output the value of stab.

 

Sample Input

 

Sample Output

 

Source

 

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#include<cstdio>

#include<iostream>

#include<vector>

#include<cstring>

#include<algorithm>

#define MAX_N 5555

using namespace std;

vector<int> G[MAX_N];

bool vis[MAX_N];

int dfn[MAX_N],low[MAX_N],ind=;

int cut[MAX_N];

int node;

void Tarjan(int u,int p){

    int child=;

    dfn[u]=low[u]=++ind;

    vis[u]=;

    for(int i=;i<G[u].size();i++){

        int v=G[u][i];

        if(v==p||v==node)continue;

        if(!vis[v]){

            Tarjan(v,u);

            low[u]=min(low[v],low[u]);

            child++;

            if((p==-&&child>)||(p!=-&&low[v]>=dfn[u]))

                cut[u]++;

        }

        else

            low[u]=min(dfn[v],low[u]);

    }

}

int n,m;

void init(){

    for(int i=;i<=n;i++)G[i].clear();

    ind=;

    memset(vis,,sizeof(vis));

    memset(cut,,sizeof(cut));

}

bool used[MAX_N];

int cu;

void dfs(int u,int p){

    if(u==p||used[u]||u==node||u==cu)return;

    used[u]=;

    for(int i=;i<G[u].size();i++)dfs(G[u][i],u);

}

int main(){

    while(scanf("%d%d",&n,&m)==){

        int stab=;

        init();

        int u,v;

        for(int i=;i<m;i++) {

            scanf("%d%d", &u, &v);

            G[u].push_back(v);

            G[v].push_back(u);

        }

        for(int i=;i<n;i++){

            node=i;

            memset(vis,,sizeof(vis));

            ind=;

            memset(cut,,sizeof(cut));

            for(int j=;j<n;j++)

                if((!vis[j])&&j!=node)

                    Tarjan(j,-);

            int maxC=;

            for(int j=;j<n;j++)

                if(j!=node&&cut[j]>=maxC){

                    cu=j;

                    maxC=cut[j];

                }

            int ans=;

            memset(used,,sizeof(used));

            for(int j=;j<n;j++)

                if((!used[j])&&j!=node&&j!=cu){

                    dfs(j,-);

                    ans++;

                }

            stab=max(stab,ans);

        }

        printf("%d\n",stab);

    }

    return ;

}