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>
using namespace std;
typedef long long LL;
const int mxn=1000010;
int M,n,m,head[mxn],fa[mxn],stk[mxn],rnk[mxn],a[mxn],b[mxn];
LL f[mxn],g[mxn];
bool cmp(const int &x,const int &y){return a[x]<a[y];}
struct ed{int to,nxt;}edge[mxn];
void addedge(int u,int v){
	edge[++M]=(ed){v,head[u]},head[u]=M;
	edge[++M]=(ed){u,head[v]},head[v]=M;
}
int find(int x){
	if (fa[x]==x) return x;
	else return fa[x]=find(fa[x]);
}
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=n;++i) fa[i]=i,stk[i]=i;
	for (int i=1;i<=n;++i)
		scanf("%d%d",&a[i],&b[i]),a[i]=max(a[i]-b[i],0);
	sort(stk+1,stk+n+1,cmp);
	for (int i=1;i<=n;++i) rnk[stk[i]]=i;
	for (int i=1,x,y;i<=m;++i)
		scanf("%d%d",&x,&y),addedge(x,y);
	for (int j=1,u;j<=n;++j){
		u=stk[j],g[u]=b[u];
		LL mn=a[u];
		for (int i=head[u];i;i=edge[i].nxt){
			int v=edge[i].to,fx=find(v);
			if (fx!=u&&rnk[v]<rnk[u])
				g[u]+=g[fx],mn=min(mn,max(1ll*a[u],f[fx])-g[fx]),fa[fx]=u;
		}
		f[u]=g[u]+mn;
	}
	printf("%lld\n",f[stk[n]]);
	return 0;
}