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 <bits/stdc++.h>
const int N=1e5+5;
int to[N],Next[N],last[N],a[N],b[N],n,m,id[N],edge,x,y,f[N],vis[N];
long long sum[N],dp[N];
std::vector<int> e[N];
bool cmp(int x,int y){
	return a[x]<a[y];
}
void add(int x,int y){
	to[++edge]=y;
	Next[edge]=last[x];
	last[x]=edge;
}
void dfs(int x){
	sum[x]=b[x];
	for (int i=last[x];i;i=Next[i]){
		int u=to[i];
		dfs(u);	
		sum[x]+=sum[u];
	}
}
void Dfs(int x){
	dp[x]=a[x]+sum[x];
	for (int i=last[x];i;i=Next[i]){
		int u=to[i];
		Dfs(u);
		dp[x]=std::min(dp[x],std::max(a[x]*1ll,dp[u])+sum[x]-sum[u]);
	}
}
int find(int x){
	if (f[x]==x) return x;
	f[x]=find(f[x]);
	return f[x];
}
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],0);
	}
	for (int i=1;i<=n;i++) id[i]=i;
	std::sort(id+1,id+n+1,cmp);
	for (int i=1;i<=m;i++){
		scanf("%d%d",&x,&y);
		e[x].push_back(y),e[y].push_back(x);	
	}
	for (int i=1;i<=n;i++) f[i]=i;
	for (int i=1;i<=n;i++){
		int x=id[i];
		vis[x]=1;
		for (auto j:e[x])
			if (vis[j]==1){
				int ff=find(j);
				if (ff!=x) add(x,ff),f[ff]=x;
			}
	}
	dfs(id[n]);	
	Dfs(id[n]);
	printf("%lld\n",dp[id[n]]);
}