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>
#define ll long long
using namespace std;
int n,m,x,y,a[100001],b[100001],f[100001],p[100001],bz[100001],o;
ll c[100001],dp[100001],sum[100001];
int hed[100001],too[200001],nxt[200001],tot;
void link(int x,int y)
{
	nxt[++tot]=hed[x];
	too[tot]=y;
	hed[x]=tot;
}
int find(int x)
{
	return f[x]=(x==f[x]?x:find(f[x]));
}
bool cmp(int x,int y)
{
	return c[x]<c[y];
}
int main()
{
	scanf("%d %d",&n,&m);
	for (int i=1;i<=n;i++)scanf("%d %d",&a[i],&b[i]),c[i]=max(0,a[i]-b[i]),p[i]=f[i]=i,sum[i]=b[i];
	for (int i=1;i<=m;i++)scanf("%d %d",&x,&y),link(x,y),link(y,x);
	sort(p+1,p+1+n,cmp);
	for (int i=1;i<=n;i++)
	{
		vector<int> son;
		int u=p[i];
		bz[u]=1;
		for (int vv=hed[u];vv;vv=nxt[vv])
		{
			int v=too[vv];
			if (bz[v])
			{
				int x=find(u),y=find(v);
				if (x!=y)sum[u]+=sum[y],f[y]=u,son.push_back(y);
			}
		}
		dp[u]=c[u]+sum[u];
		for (int j=0;j<son.size();j++)o=son[j],dp[u]=min(dp[u],sum[u]-sum[o]+max(c[u],dp[o]));
	}
	printf("%lld\n",dp[find(1)]);
}