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>
using namespace std;
typedef long long ll;
#define REP(i,a,b) for(int i=(a),ed=(b);i<=ed;++i)
#define pb(x) push_back((x))
inline int read(){
	register int x=0,f=1;register char ch=getchar();
	while(!isdigit(ch)){if(ch=='-')f=0;ch=getchar();}
	while(isdigit(ch)){x=x*10+(ch^'0');ch=getchar();}
	return f?x:-x;
}

const int N=1e5+10;
int n,m,p[N],vis[N],f[N],head[N],num;
inline int find(int x){return f[x]=f[x]==x?f[x]:find(f[x]);}
struct edge{int to,next;}e[N<<1];
inline void add(int u,int v){e[++num]=(edge){v,head[u]},head[u]=num;}
vector<int> E[N];
ll dp[N],s[N],a[N],b[N],w[N];
inline bool cmp_w(const int &a,const int &b){return w[a]<w[b];}

inline void Dfs(int u){
	s[u]=b[u];
	for(int v:E[u]){
		Dfs(v);s[u]+=s[v];
	}
	if(s[u]==b[u]){dp[u]=b[u]+w[u];return;}
	for(int v:E[u]){
		dp[u]=min(dp[u],s[u]-s[v]+max(w[u],dp[v]));
	}
}

int main(){
	//freopen("in.in","r",stdin);
	n=read(),m=read();
	REP(i,1,n)a[i]=read(),b[i]=read(),w[i]=max(a[i]-b[i],0ll),p[i]=i;
	REP(i,1,m){
		int u=read(),v=read();
		add(u,v),add(v,u);
	}
	REP(i,1,n)f[i]=i;
	sort(p+1,p+n+1,cmp_w);
	REP(i,1,n){
		vis[p[i]]=1;
		for(int j=head[p[i]];j;j=e[j].next){
			if(!vis[e[j].to])continue;
			int x=find(e[j].to);
			if(x^p[i])f[x]=p[i],E[p[i]].pb(x);
		}
	}
	int pa=find(1);
	REP(i,1,n)dp[i]=1e18;
	Dfs(pa);
	printf("%lld\n",dp[pa]);
	return 0;
}
