Codeforces Round #614 (Div. 2) E. Xenon's Attack on the Gangs

http://codeforces.com/contest/1293/problem/E

题意：

给出一棵n个点的树，将0—n-2作为边权，最大化 Σ mex(u,v)

mex(u,v) 表示u到v的路径上最小的未出现过的自然数

将[0,m]加到一条链上，且这条链上加的边权大小呈一个向上凸起的单峰函数状

那么我们可以依次得到[1,m+1]的贡献

原问题转化成 Σ f(x)，f(x)表示 mex(u,v) >=x的(u,v)对数

令sub[u][v]表示以u为根时，v的子树大小

fa[u][v]表示以u为根时，v的父节点

dp[u][v]表示从u到v的一条链的答案

Σ f(x) x∈[1,m] = f(m)+Σ f(x) x∈[1,m-1] = sub[u][v]*sub[v][u] + max ( dp[u][fa[u][v]] ,dp[v][fa[v][u]])

#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

#define N 3001

int sub[N][N],fa[N][N];
long long dp[N][N];

int tot,front[N],nxt[N<<1],to[N<<1];

void add(int u,int v)
{
    to[++tot]=v; nxt[tot]=front[u]; front[u]=tot;
    to[++tot]=u; nxt[tot]=front[v]; front[v]=tot;
}

void dfs(int root,int x,int f)
{
    sub[root][x]=1;
    int t;
    for(int i=front[x];i;i=nxt[i])
    {
        t=to[i];
        if(t!=f)
        {
            fa[root][t]=x;
            dfs(root,t,x);
            sub[root][x]+=sub[root][t];
        }
    }
}

long long getans(int u,int v)
{
    if(u==v) return 0; 
    if(dp[u][v]!=-1) return dp[u][v];
    long long k1=getans(u,fa[u][v]),k2=getans(v,fa[v][u]);
    dp[u][v]=sub[u][v]*sub[v][u]+max(k1,k2);
    return dp[u][v];
}

int main()
{
    int n,u,v;
    scanf("%d",&n);
    for(int i=1;i<n;++i)
    {
        scanf("%d%d",&u,&v);
        add(u,v);
    }
    for(int i=1;i<=n;++i) dfs(i,i,0);
    memset(dp,-1,sizeof(dp));
    long long ans=0;
    for(int i=1;i<=n;++i)
        for(int j=1;j<=n;++j)
        {
            dp[i][j]=getans(i,j);
            ans=max(ans,dp[i][j]);
        }
    printf("%lld",ans);
    return 0;
}

INSPION FullBand Master - INSPION

INSPION - IOLITE-SUNSTONE

On another floor of the A.R.C. Markland-N, the young man Simon "Xenon" Jackson, takes a break after finishing his project early (as always). Having a lot of free time, he decides to put on his legendary hacker "X" instinct and fight against the gangs of the cyber world.

His target is a network of

By mining data, Xenon figured out that the gangs used a form of cross-encryption to avoid being busted: every link was assigned an integer from

S=\sum1\lequ<v\leqnmex(u,v)

Here,

Xenon doesn't know the way the integers are assigned, but it's not a problem. He decides to let his AI's instances try all the passwords on his behalf, but before that, he needs to know the maximum possible value of

Now, Xenon is out to write the AI scripts, and he is expected to finish them in two hours. Can you find the maximum possible

Input

The first line contains an integer

Each of the next

It's guaranteed that links are placed in such a way that each pair of gangs will be connected by exactly one simple path.

Output

Print the maximum possible value of

Examples

Input

Copy

3
1 2
2 3

Output

Copy

Input

Copy

Output

Copy

Note

In the first example, one can achieve the maximum

$Codeforces Round #614 (Div. 2) E. Xenon's Attack on the Gangs$

With this assignment,

In the second example, one can achieve the maximum

$Codeforces Round #614 (Div. 2) E. Xenon's Attack on the Gangs$

With this assignment, all non-zero mex value are listed below:

Therefore,