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 <cstring>
#include <algorithm>

long long a[100001],n,m,head[100001],nxt[200001],b[200001],k,fa[100001];
long long B[100001],f[100001];
bool vis[100001];
void push(int s,int t){
	nxt[++k]=head[s];
	head[s]=k;
	b[k]=t;
}
int find(int x){return f[x]?f[x]=find(f[x]):x;}
std::pair<int,int>p[100001];
void dfs(int x){
	for(int i=head[x];i;i=nxt[i])dfs(b[i]),B[x]+=B[b[i]];
	f[x]=a[x]+B[x];
	for(int i=head[x];i;i=nxt[i])f[x]=std::min(f[x],B[x]-B[b[i]]+std::max(a[x],f[b[i]]));
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)scanf("%d%d",a+i,B+i),a[i]=std::max(a[i]-B[i],0ll),p[i]=std::make_pair(a[i],i);
	for(int i=1,u,v;i<=m;i++)scanf("%d%d",&u,&v),push(u,v),push(v,u);
	std::sort(p+1,p+n+1);
	for(int i=1;i<=n;i++){
		int u=p[i].second;
		for(int j=head[u];j;j=nxt[j])
			if(vis[b[j]]&&find(b[j])!=find(u)){
				int fu=find(b[j]);
				fa[fu]=u;
				f[fu]=u;
			}
		vis[u]=1;
	}
	memset(head,0,sizeof head);
	k=0;
	int root;
	for(int i=1;i<=n;i++)(fa[i])?push(fa[i],i),0:root=i;
	dfs(root);
	printf("%lld\n",f[root]);
}