1 #include<algorithm>
 2 #include<iostream>
 3 #include<cstring>
 4 #include<cstdio>
 5 //by NeighThorn
 6 #define inf 0x3f3f3f3f
 7 #define INF 0x3f3f3f3f3f3f3f3f
 8 using namespace std;
 9 
10 const int maxn=200+5,maxm=100000+5;
11 
12 int n,m,S,T,cnt,sum,a[maxn],b[maxn],hd[maxn*2],fl[maxm],to[maxm],nxt[maxm],pos[maxn*2];
13 long long dis[maxn][maxn],Max;
14 
15 inline void add(int s,int x,int y){
16     fl[cnt]=s;to[cnt]=y;nxt[cnt]=hd[x];hd[x]=cnt++;
17     fl[cnt]=0;to[cnt]=x;nxt[cnt]=hd[y];hd[y]=cnt++;
18 }
19 
20 inline bool bfs(void){
21     memset(pos,-1,sizeof(pos));
22     int head=0,tail=0,q[maxn*2];
23     q[0]=S,pos[S]=0;
24     while(head<=tail){
25         int top=q[head++];
26         for(int i=hd[top];i!=-1;i=nxt[i])
27             if(pos[to[i]]==-1&&fl[i])
28                 pos[to[i]]=pos[top]+1,q[++tail]=to[i];
29     }
30     return pos[T]!=-1;
31 }
32 
33 inline int find(int v,int f){
34     if(v==T)
35         return f;
36     int res=0,t;
37     for(int i=hd[v];i!=-1&&f>res;i=nxt[i])
38         if(pos[to[i]]==pos[v]+1&&fl[i])
39             t=find(to[i],min(fl[i],f-res)),fl[i]-=t,fl[i^1]+=t,res+=t;
40     if(!res)
41         pos[v]=-1;
42     return res;
43 }
44 
45 inline int dinic(void){
46     int res=0,t;
47     while(bfs())
48         while(t=find(S,inf))
49             res+=t;
50     return res;
51 }
52 
53 inline int check(long long mid){
54     cnt=0;memset(hd,-1,sizeof(hd));
55     for(int i=1;i<=n;i++)
56         add(a[i],S,i+n),add(b[i],i,T),add(inf,i+n,i);
57     for(int i=1;i<=n;i++)
58         for(int j=1;j<=n;j++)
59             if(dis[i][j]<=mid)
60                 add(inf,i+n,j);
61     return dinic();
62 }
63 
64 signed main(void){
65 //    freopen("in.txt","r",stdin);
66     Max=0,sum=cnt=0;
67     scanf("%d%d",&n,&m);
68     S=0,T=n*2+1;
69     for(int i=1;i<=n;i++)
70         for(int j=1;j<=n;j++)
71             dis[i][j]=INF;
72     for(int i=1;i<=n;i++)
73         scanf("%d%d",&a[i],&b[i]),sum+=a[i];
74     for(int i=1,s,x,y;i<=m;i++)
75         scanf("%d%d%d",&x,&y,&s),dis[x][y]=dis[y][x]=min(dis[x][y],(long long)s);
76     for(int k=1;k<=n;k++)
77         for(int i=1;i<=n;i++)
78             for(int j=1;j<=n;j++)
79                 dis[i][j]=min(dis[i][j],dis[i][k]+dis[k][j]);
80     long long l=0,r=INF-1,ans=-1;
81     while(l<=r){
82         long long mid=(l+r)>>1;
83         if(check(mid)==sum)
84             ans=mid,r=mid-1;
85         else
86             l=mid+1;
87     }
88     printf("%lld\n",ans);
89     return 0;  
90 }//Cap ou pas cap. Cap.