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<algorithm>
#include<vector>
#define int long long
int n,m,a[100100],b[100100],fa[100100],id[100100],vis[100100],sum[100100],cnt[100100];
std::vector<int> e[100100]; 
bool cmp(int x,int y){
	return a[x]<a[y];
} 
int find(int x){
	if(x==fa[x])return x;
	return fa[x]=find(fa[x]);
}
signed main(){
	scanf("%lld%lld",&n,&m);
	for(int i=1;i<=n;i++){
		scanf("%lld%lld",&a[i],&b[i]);
		a[i]=std::max(a[i]-b[i],0ll);
		cnt[i]=a[i];
		sum[i]=b[i];
		fa[i]=id[i]=i;
		vis[i]=0;
	}
	for(int i=1,x,y;i<=m;i++){
		scanf("%lld%lld",&x,&y);
		e[x].push_back(y);
		e[y].push_back(x);
	}
	std::sort(id+1,id+n+1,cmp);
	for(int i=1;i<=n;i++){
		int x=id[i];
		vis[x]=1;
		for(int j=0;j<e[x].size();j++){
			int upup=e[x][j];
			if(vis[upup]){
				int rx=find(x),ry=find(upup);
				if(rx!=ry){
					fa[ry]=rx;
					sum[rx]+=sum[ry];
					cnt[rx]=std::min(cnt[rx],cnt[ry]+std::max(0ll,a[rx]-cnt[ry]-sum[ry]));
				}
			}
		}
	}
	printf("%lld",cnt[id[n]]+sum[id[n]]);
	return 0;
}