/*      最大流SAP      邻接表      思路：基本源于FF方法，给每个顶点设定层次标号，和允许弧。      优化:      1、当前弧优化（重要）。      1、每找到以条增广路回退到断点（常数优化）。      2、层次出现断层，无法得到新流（重要）。      时间复杂度（m*n^2）*/#include <iostream>#include <cstdio>#include <cstring>#define ms(a,b) memset(a,b,sizeof a)using namespace std;const int INF = 500;long long G[INF][INF];struct node {    int v, c, next;} edge[INF*INF * 4];long long  pHead[INF*INF], SS, ST, nCnt;void addEdge (int u, int v, int c) {    edge[++nCnt].v = v; edge[nCnt].c = c, edge[nCnt].next = pHead[u]; pHead[u] = nCnt;    edge[++nCnt].v = u; edge[nCnt].c = 0, edge[nCnt].next = pHead[v]; pHead[v] = nCnt;}int SAP (int pStart, int pEnd, int N) {    int numh[INF], h[INF], curEdge[INF], pre[INF];    int cur_flow, flow_ans = 0, u, neck, i, tmp;    ms (h, 0); ms (numh, 0); ms (pre, -1);    for (i = 0; i <= N; i++) curEdge[i] = pHead[i];    numh[0] = N;    u = pStart;    while (h[pStart] <= N) {        if (u == pEnd) {            cur_flow = 1e9;            for (i = pStart; i != pEnd; i = edge[curEdge[i]].v)                if (cur_flow > edge[curEdge[i]].c) neck = i, cur_flow = edge[curEdge[i]].c;            for (i = pStart; i != pEnd; i = edge[curEdge[i]].v) {                tmp = curEdge[i];                edge[tmp].c -= cur_flow, edge[tmp ^ 1].c += cur_flow;            }            flow_ans += cur_flow;            u = neck;        }        for ( i = curEdge[u]; i != 0; i = edge[i].next)            if (edge[i].c && h[u] == h[edge[i].v] + 1)     break;        if (i != 0) {            curEdge[u] = i, pre[edge[i].v] = u;            u = edge[i].v;        }        else {            if (0 == --numh[h[u]]) continue;            curEdge[u] = pHead[u];            for (tmp = N, i = pHead[u]; i != 0; i = edge[i].next)                if (edge[i].c)  tmp = min (tmp, h[edge[i].v]);            h[u] = tmp + 1;            ++numh[h[u]];            if (u != pStart) u = pre[u];        }    }    return flow_ans;}long long m, n, x, y,sum,c;int in[INF], out[INF];bool check (long long tem) {    nCnt = 1;    SS = 2 * n + 1, ST = 2 * n + 2;    memset (pHead, 0, sizeof pHead);    for (int i = 1; i <= n; i++) {        if(out[i]) addEdge (SS, i, out[i]);        for (int j =1; j <= n; j++)            if (G[i][j] <= tem&&G[i][j]!=-1)                addEdge (i, j+n, 5000);    }    for (int i = 1; i <= n; i++)              if(in[i])addEdge (i + n, ST, in[i]);    int ans = SAP (SS, ST, ST);    if (ans == sum) return 1;    return 0;}int main() {    /*           建图,前向星存边，表头在pHead[],边计数 nCnt.           SS,ST分别为源点和汇点    */    ms (G, -1);    cin>>n>>m;    for (int i = 1; i <= n; i++) {        cin>>out[i]>>in[i];        sum += out[i];    }    long long l = 0x7fffffffffffffff, r = 0;    for (int i = 1; i <= n; i++) G[i][i] = 0;    for (int i = 1; i <= m; i++) {        cin>>x>>y>>c;        if(G[x][y]>0) G[x][y] = G[y][x] = min(c,G[x][y]);        else                     G[x][y]=G[y][x]=c;        l = min (l, c), r = max (r, c);    }    for (int  t = 1; t <= n; t++)        for (int i = 1; i <= n; i++)            for (int j = 1; j <= n; j++) {                if (G[i][t] == -1 || G[t][j] == -1) continue;                if (G[i][j] == -1 || G[i][j] > G[i][t] + G[t][j])                    G[i][j] = G[i][t] + G[t][j], l = min (l, G[i][j]), r = max (r, G[i][j]);            }    long long last = -1,mid;    while (l <= r) {        mid = (l + r) >> 1;        if (check (mid) ) {            last = mid;            r = mid - 1;        }        else l = mid + 1;    }    cout<<last;    return 0;}