There is a simple undirected graph with N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i connects Vertex U_i and V_i. Also, Vertex i has two predetermined integers A_i and B_i. You will play the following game on this graph.

First, choose one vertex and stand on it, with W yen (the currency of Japan) in your pocket. Here, A_s \leq W must hold, where s is the vertex you choose. Then, perform the following two kinds of operations any number of times in any order:

* Choose one vertex v that is directly connected by an edge to the vertex you are standing on, and move to vertex v. Here, you need to have at least A_v yen in your pocket when you perform this move.
* Donate B_v yen to the vertex v you are standing on. Here, the amount of money in your pocket must not become less than 0 yen.



You win the game when you donate once to every vertex. Find the smallest initial amount of money W that enables you to win the game.

Constraints

* 1 \leq N \leq 10^5
* N-1 \leq M \leq 10^5
* 1 \leq A_i,B_i \leq 10^9
* 1 \leq U_i < V_i \leq N
* The given graph is connected and simple (there is at most one edge between any pair of vertices).

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
A_2 B_2
:
A_N B_N
U_1 V_1
U_2 V_2
:
U_M V_M


Output

Print the smallest initial amount of money W that enables you to win the game.

Examples

Input

4 5
3 1
1 2
4 1
6 2
1 2
2 3
2 4
1 4
3 4


Output

6


Input

5 8
6 4
15 13
15 19
15 1
20 7
1 3
1 4
1 5
2 3
2 4
2 5
3 5
4 5


Output

44


Input

9 10
131 2
98 79
242 32
231 38
382 82
224 22
140 88
209 70
164 64
6 8
1 6
1 4
1 3
4 7
4 9
3 7
3 9
5 9
2 5


Output

582
#include<cstdio>
#include<vector>
#include<algorithm>
long long a[100005], b[100005];
long long c[100005];
int order[100005];
long long sum[100005], p[100005];
std::vector<int>g[100005];
std::vector<int>e[100005];
int vis[100005];
long long f[100005];

long long min(long long a,long long b){ return a>b?b:a; }

long long max(long long a,long long b){ return a>b?a:b; }

int find(int u){
    if(p[u]==u) return u;
    else return p[u] = find(p[u]);
}

void dp(int u){
    sum[u] = b[u];
    for(int v: e[u]){
        dp(v);
        sum[u] += sum[v];
    }
    f[u] = c[u]+sum[u];
    for(int v: e[u]){
        f[u] = min(f[u],max(f[v],c[u])+sum[u]-sum[v]);
    }
}

int cmp(int a,int b){ return c[a]<c[b]; }

int main(){
    int n,m;
    scanf("%d%d",&n,&m);
    for(int i = 1; i <= n; i++){
        order[i] = p[i] = i;
        sum[i] = 0;
        scanf("%lld%lld",&a[i],&b[i]);
        c[i] = a[i]-b[i];
        if(c[i]<0) c[i] = 0;
    }
    for(int i = 0; i < m; i++){
        int u,v;
        scanf("%d%d",&u,&v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
    std::sort(order+1,order+1+n,cmp);
    for(int i = 1; i <= n; i++){
        int u = order[i]; 
        vis[u] = 1;
        for(int v: g[u]){
            if(vis[v] && find(v)!=u){
                int root = find(v);
                p[root] = u;
                //sum[u] += sum[root];
                e[u].push_back(root);
            }
        }
    }
    //printf("ok\n");
    int root = find(1);
    dp(root);
    printf("%lld\n",f[root]);
    return 0;
}
