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;
const int maxn=1e5+10;
int n,m,a[maxn],b[maxn],c[maxn],x[maxn],dsu[maxn];
ll sum[maxn],f[maxn];
vector<int> g[maxn];
bool vis[maxn];

inline bool cmp(int a,int b){
	return c[a]<c[b];
}
int find(int x){
	return dsu[x]==x?x:dsu[x]=find(dsu[x]);
}

int main(){
	cin>>n>>m;
	for(int i=1;i<=n;++i){
		cin>>a[i]>>b[i];
		c[i]=max(a[i]-b[i],0);
		x[i]=i;
		dsu[i]=i;
	}
	for(int i=1,u,v;i<=m;++i){
		cin>>u>>v;
		g[u].push_back(v);
		g[v].push_back(u);
	}
	sort(x+1,x+n+1,cmp);
	for(int i=1;i<=n;++i){
		int pos=x[i];
		sum[pos]=b[pos];
		f[pos]=c[pos];
		vis[pos]=true;
		for(int j=0,v;j<g[pos].size();++j)
			if(vis[v=find(g[pos][j])]&&v!=find(pos)){
				dsu[v]=pos;
				sum[pos]+=sum[v];
				f[pos]=min(f[pos],max(f[v],c[pos]-sum[v]));
			}
	}
	cout<<sum[find(1)]+f[find(1)]<<endl;
	return 0;
}