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<cmath>
#include<cstring>
#define ll long long
using namespace std;
const int N=100100;
int n,m,a[N],b[N],tot,Next[N<<1],head[N],tree[N<<1],f[N];
ll ans[N],g[N];
bool vis[N];
struct node{int x,y;}A[N];
void add(int x,int y)
{
	tot++;
	Next[tot]=head[x];
	head[x]=tot;
	tree[tot]=y;
}
bool cmp(node a,node b) { return a.x<b.x;}
int get(int x)
{
	if (f[x]==x) return x;else f[x]=get(f[x]);
	return f[x];
}
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=n;i++)
	{
		scanf("%d%d",&a[i],&b[i]);
		a[i]=max(0,a[i]-b[i]);
		A[i]=(node){a[i],i};
	}
	for (int i=1;i<=m;i++)
	{
		int x,y;
		scanf("%d%d",&x,&y);
		add(x,y);add(y,x);
	}
	sort(A+1,A+n+1,cmp);
	for (int i=1;i<=n;i++)
	{
		f[i]=i;
		ans[i]=a[i];
		g[i]=b[i];
	}
	for (int i=1;i<=n;i++)
	{
		int u=A[i].y;
		vis[u]=1;
		for (int j=head[u];j;j=Next[j])
		{
			int v=tree[j],x=get(v);
			if (x==u||!vis[x]) continue;
			f[x]=u;
			g[u]+=g[x];
			ans[u]=min(ans[u],max(ans[x],a[u]-g[x]));
		}
	}
	printf("%lld\n",ans[A[n].y]+g[A[n].y]);
	return 0;
}
