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<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#define ll long long
using namespace std;
inline int read(){
	int x=0,f=1;char ch;
	do{ch=getchar();if(ch=='-')f=-1;}while(ch<'0'||ch>'9');
	do{x=x*10+ch-'0';ch=getchar();}while(ch>='0'&&ch<='9');
	return x*f;
}
const int N=100010;
const ll INF=0x3f3f3f3f3f3f3f3f;
struct node{
	int v,next;
}edge[N<<1];
int last[N],le;
void add(int u,int v){
	edge[++le].v=v,edge[le].next=last[u],last[u]=le;
	edge[++le].v=u,edge[le].next=last[v],last[v]=le;
}
ll a[N],b[N],dp[N],sum[N];
int f[N],fa[N],pos[N],rt;
inline int find(int x){
	return f[x]==x?x:f[x]=find(f[x]);
}
inline bool cmp(int t1,int t2){
	return a[t1]<a[t2];
}
vector<int> G[N];
void dfs(int u){
	sum[u]=b[u];
	if (!G[u].size()){
		dp[u]=a[u]+b[u];
		return;
	}
	for (int i=G[u].size()-1;~i;--i){
		int v=G[u][i];
		dfs(v);
		sum[u]+=sum[v];
	}
	dp[u]=INF;
	for (int i=G[u].size()-1;~i;--i){
		int v=G[u][i];
		dp[u]=min(dp[u],max(dp[v],a[u])+sum[u]-sum[v]);
	}
}
int main(){
	int n=read(),m=read();
	for (int i=1;i<=n;++i){
		a[i]=read(),b[i]=read();
		a[i]=max(a[i]-b[i],0ll);
		pos[i]=f[i]=i,fa[i]=-1;
	}
	for (int i=1;i<=m;++i){
		int u=read(),v=read();
		add(u,v);
	}
	sort(pos+1,pos+n+1,cmp);
	for (int j=1;j<=n;++j){
		int u=pos[j];
		for (int i=last[u];i;i=edge[i].next){
			int v=edge[i].v;
			if (fa[find(v)]==0) fa[find(v)]=f[find(v)]=u;
		}
		fa[u]=0;
	}
	for (int i=1;i<=n;++i){
		if (!fa[i]) rt=i;
		else G[fa[i]].push_back(i);
	}
	dfs(rt);
	printf("%lld\n",dp[rt]);
	return 0;
}