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,doe;
int fa[101010],id[101010];
int pre[202020],son[202020],now[101010];
ll a[101010],b[101010],f[101010],sum[101010];
bool br[101010];
int find(int x)
{
	if (fa[x]==x) return fa[x];
	fa[x]=find(fa[x]);
	return fa[x];
}
void add(int x,int y)
{
	++doe;
	pre[doe]=now[x];
	now[x]=doe;
	son[doe]=y;
}
bool cmp(int u,int w)
{
	return a[u]<a[w];
}
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=n;++i) scanf("%lld%lld",&a[i],&b[i]),a[i]=max(a[i]-b[i],0ll);
	int x,y;
	for (int i=1;i<=m;++i) scanf("%d%d",&x,&y),add(x,y),add(y,x);
	
	for (int i=1;i<=n;++i) id[i]=i,fa[i]=i,f[i]=a[i],sum[i]=b[i];
	sort(id+1,id+1+n,cmp);

	for (int i=1;i<=n;++i)
	{
		x=id[i];
		br[x]=1;
		int p=now[x];
		while (p)
		{
			int y=son[p];
			if (br[y])
			{
				int xx=find(x),yy=find(y);
				if (xx!=yy)
				{
					fa[yy]=xx;
					sum[xx]+=sum[yy];
					f[xx]=min(f[xx],max(f[yy],a[xx]-sum[yy]));
				}
			}
			p=pre[p];
		}
	}
	printf("%lld\n",sum[id[n]]+f[id[n]]);
	return 0;
}

