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<algorithm> 
using namespace std;
struct node
{
	long long v,nxt;
};
node edge[200001];
struct reads
{
	long long num,data;
	bool operator < (const reads &a)const
	{
		return data<a.data;
	}
};
reads t[100001];
long long n,m,a[100001],b[100001],head[100001],len,rt[100001],sz[100001],Mx[100001];
int find(int x)
{
	if (rt[x]==x)
		return x;
	return rt[x]=find(rt[x]);
}
void unionn(int x,int y)
{
	sz[find(y)]+=sz[find(x)];
	Mx[find(y)]=min(Mx[find(y)],max(Mx[find(x)],a[find(y)]-b[find(y)]-sz[find(x)]));
	rt[find(x)]=find(y);
	return;
}
void add(int x,int y)
{
	edge[++len].v=y;
	edge[len].nxt=head[x];
	head[x]=len;
	return;
}
int main()
{
	int x,y;
	cin>>n>>m;
	for (int i=1;i<=n;++i)
	{
		cin>>a[i]>>b[i];
		rt[i]=i;
		sz[i]=b[i];
		t[i].num=i;
		Mx[i]=max(a[i]-b[i],0ll);
		t[i].data=Mx[i];
	}
	for (int i=1;i<=m;++i)
	{
		cin>>x>>y;
		add(x,y);
		add(y,x);
	}
	sort(t+1,t+n+1);
	for (int i=1;i<=n;++i)
		for (int j=head[t[i].num];j>0;j=edge[j].nxt)
			if (a[t[i].num]>=a[edge[j].v]&&find(edge[j].v)!=find(t[i].num))
				unionn(edge[j].v,t[i].num);
	cout<<Mx[find(1)]+sz[find(1)]<<endl;
	return 0;
}