C++ :

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=5005;
const int inf=1000000000;

int n,cnt,last[N],mn,val,mx1[N],mx2[N],bel1[N],bel2[N];
struct edge{int to,next,w;}e[N*2];

int read()
{
    int x=0,f=1;char ch=getchar();
    while (ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while (ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}

void addedge(int u,int v,int w)
{
    e[++cnt].to=v;e[cnt].w=w;e[cnt].next=last[u];last[u]=cnt;
    e[++cnt].to=u;e[cnt].w=w;e[cnt].next=last[v];last[v]=cnt;
}

void get_dia(int x,int fa)
{
    mx1[x]=mx2[x]=0;
    for (int i=last[x];i;i=e[i].next)
    {
        if (e[i].to==fa) continue;
        get_dia(e[i].to,x);
        if (mx1[e[i].to]+e[i].w>mx1[x]) mx2[x]=mx1[x],mx1[x]=mx1[e[i].to]+e[i].w;
        else if (mx1[e[i].to]+e[i].w>mx2[x]) mx2[x]=mx1[e[i].to]+e[i].w;
    }
    val=max(val,mx1[x]+mx2[x]);
}

void get_cen1(int x,int fa)
{
    mx1[x]=mx2[x]=0;
    for (int i=last[x];i;i=e[i].next)
    {
        if (e[i].to==fa) continue;
        get_cen1(e[i].to,x);
        int v=mx1[e[i].to]+e[i].w,id=e[i].to;
        if (v>mx1[x]) mx2[x]=mx1[x],bel2[x]=bel1[x],mx1[x]=v,bel1[x]=id;
        else if (v>mx2[x]) mx2[x]=v,bel2[x]=id;
    }
}

void get_cen2(int x,int fa)
{
    mn=min(mn,mx1[x]);
    for (int i=last[x];i;i=e[i].next)
    {
        if (e[i].to==fa) continue;
        int v,to=e[i].to;
        if (bel1[x]==e[i].to) v=mx2[x]+e[i].w;
        else v=mx1[x]+e[i].w;
        if (v>mx1[to]) mx2[to]=mx1[to],bel2[to]=bel1[to],mx1[to]=v,bel1[to]=x;
        else if (v>mx2[to]) mx2[to]=v,bel2[to]=x;
        get_cen2(e[i].to,x);
    }
}

int main()
{
    n=read();
    for (int i=1;i<n;i++)
    {
        int x=read(),y=read(),z=read();
        addedge(x,y,z);
    }
    int ans=inf;
    for (int i=1;i<n;i++)
    {
        int x=e[i*2-1].to,y=e[i*2].to,z=e[i*2].w;
        val=0;get_dia(x,y);get_dia(y,x);
        mn=inf;get_cen1(x,y);get_cen2(x,y);
        int tmp=mn;
        mn=inf;get_cen1(y,x);get_cen2(y,x);
        val=max(val,tmp+mn+z);
        ans=min(ans,val);
    }
    printf("%d",ans);
    return 0;
}