#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;int n;
struct sc
{int x,y,d;
}e[21000];int mp[1100][1100];
bool istree[21000];
struct node
{int x,y,d,id,next;
}a[21000];int len,last[21000];
void ins(int x,int y,int d,int id)
{len++;a[len].x=x;a[len].y=y;a[len].d=d;a[len].id=id;a[len].next=last[x];last[x]=len;
}
int fa[1100],dep[1100],pre[11000];
void dfs(int x,int fr)
{for(int k=last[x];k;k=a[k].next){int y=a[k].y;if(y!=fr){fa[y]=x;dep[y]=dep[x]+1;pre[y]=k;dfs(y,x);}}
}
int love[1100][1100];
void build(int now,int i)
{int x=e[i].x,y=e[i].y;while(x!=y){if(dep[x]>dep[y])swap(x,y);int k=pre[y];love[now][a[k].id]=a[k].d-e[i].d;y=fa[y];}
}int exg[1100],exb[1100];
bool vg[1100],vb[1100];
int match[1100],need[1100];
bool findboy(int x)
{vg[x]=true;for(int i=1;i<=n;i++){if(vb[i]==false){int gap=exg[x]+exb[i]-love[x][i];if(gap==0){vb[i]=true;if(match[i]==0||findboy(match[i])==true){match[i]=x;return true;}}else need[i]=min(need[i],gap);}}return false;
}
void KM()
{memset(match,0,sizeof(match));memset(exg,0,sizeof(exg));memset(exb,0,sizeof(exb));for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)exg[i]=max(exg[i],love[i][j]);for(int i=1;i<=n;i++){memset(need,63,sizeof(need));while(1){memset(vg,false,sizeof(vg));memset(vb,false,sizeof(vb));if(findboy(i)==true)break;int d=2147483647;for(int j=1;j<=n;j++)if(vb[j]==false)d=min(d,need[j]);for(int j=1;j<=n;j++){if(vg[j]==true)exg[j]-=d;if(vb[j]==true)exb[j]+=d;else need[j]-=d;}}}int ans=0;for(int i=1;i<=n;i++)ans+=love[match[i]][i];printf("%d\n",ans);
}
int main()
{freopen("mst.in","r",stdin);freopen("mst.out","w",stdout);int m,x,y,d;scanf("%d%d",&n,&m);for(int i=1;i<=m;i++){scanf("%d%d%d",&e[i].x,&e[i].y,&e[i].d);mp[e[i].x][e[i].y]=i;}memset(istree,false,sizeof(istree));for(int i=1;i<n;i++){scanf("%d%d",&x,&y);int id=mp[x][y];istree[id]=true;ins(x,y,e[id].d,i);ins(y,x,e[id].d,i);}dep[1]=1;dfs(1,0);memset(love,0,sizeof(love));for(int i=1,tp=0;i<=m;i++)if(istree[i]==false)build(++tp,i);n=max(n-1,m-(n-1));KM();return 0;
}