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 fo(a,b,c) for (a=b; a<=c; a++)
#define fd(a,b,c) for (a=b; a>=c; a--)
#define min(a,b) (a<b?a:b)
#define max(a,b) (a>b?a:b)
#define ll long long
//#define file
using namespace std;

int a[200001][2],ls[100001],A[100001],B[100001],C[100001],fa[100001],n,m,i,j,k,l,len;
ll f[100001],sum[100001];
bool bz[100001];

void New(int x,int y) {++len;a[len][0]=y;a[len][1]=ls[x];ls[x]=len;}
bool cmp(int x,int y) {return C[x]>C[y];}
int gf(int t) {if (fa[t]==t) return fa[t];fa[t]=gf(fa[t]);return fa[t];}
namespace G{
	int a[200001][2],ls[100001],b[100001],len,i,j,k,l,x,y;
	
	void New(int x,int y) {++len;a[len][0]=y;a[len][1]=ls[x];ls[x]=len;}
	void work()
	{
		fo(i,1,n) b[i]=i;
		sort(b+1,b+n+1,cmp);
		fd(l,n,1)
		{
			bz[b[l]]=1;
			for (i=ls[b[l]]; i; i=a[i][1])
			if (bz[a[i][0]])
			{
				x=gf(b[l]),y=gf(a[i][0]);
				if (x!=y)
				fa[fa[y]]=fa[x],::New(x,y),::New(y,x);
			}
		}
	}
}
void dfs(int Fa,int t)
{
	int i;
	
	f[t]=9223372036854775807ll,sum[t]=B[t];
	for (i=ls[t]; i; i=a[i][1])
	if (a[i][0]!=Fa)
	dfs(t,a[i][0]),sum[t]+=sum[a[i][0]];
	
	f[t]=sum[t]+C[t];
	for (i=ls[t]; i; i=a[i][1])
	if (a[i][0]!=Fa)
	f[t]=min(f[t],sum[t]-sum[a[i][0]]+max(C[t],f[a[i][0]]));
}

int main()
{
	#ifdef file
	freopen("arc098F.in","r",stdin);
	#endif
	
	scanf("%d%d",&n,&m);
	fo(i,1,n) scanf("%d%d",&A[i],&B[i]),A[i]=max(A[i],B[i]),fa[i]=i,C[i]=A[i]-B[i];
	fo(i,1,m) scanf("%d%d",&j,&k),G::New(j,k),G::New(k,j);
	
	G::work();
	dfs(0,G::b[1]);
	printf("%lld\n",f[G::b[1]]);
	
	fclose(stdin);
	fclose(stdout);
	return 0;
}