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<cstdio>
#include<algorithm>
#include<cstring>
#include<queue>
#define ll long long
using namespace std;
struct Edge
{
	int to;
	int nxt;
}e[200005];
int p[100005],n,m,edgenum,head[100005],tmp[100005],top;
ll a[100005],b[100005];
bool flag[100005],used[100005];
priority_queue<pair<ll,int>,vector<pair<ll,int> >,greater<pair<ll,int> > >q;
void add(int u,int v)
{
	e[++edgenum].to=v;
	e[edgenum].nxt=head[u];
	head[u]=edgenum;
}
bool cmp(int x,int y)
{
	return a[x]<a[y];
}
bool bfs(int st,ll v)
{
	while(!q.empty()) q.pop();
	top=0;
	q.push(make_pair(a[st],st));
	while(!q.empty())
	{
		if(q.top().first>v)break;
		int node=q.top().second;
		q.pop();
		if(flag[node])continue;
		tmp[++top]=node;
		v+=b[node];
		flag[node]=used[node]=1;
		for(int hd=head[node];hd;hd=e[hd].nxt)
		{
			int to=e[hd].to;
			if(flag[to])continue;
			q.push(make_pair(a[to],to));
		}
	}
	for(int i=1;i<=top;i++)flag[tmp[i]]=0;
	return top==n;
}
bool check(ll v)
{
	for(int i=1;i<=n;i++)p[i]=i;
	random_shuffle(p+1,p+n+1);
	memset(used,0,sizeof(used));
	memset(flag,0,sizeof(flag));
	for(int i=1;i<=n;i++)
	{
		if(used[p[i]])continue;
		if(bfs(p[i],v))return 1;
	}
	return 0;
}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)
	{
		scanf("%lld%lld",&a[i],&b[i]);
		a[i]-=b[i];
	}
	for(int i=1;i<=m;i++)
	{
		int u,v;
		scanf("%d%d",&u,&v);
		add(u,v);
		add(v,u);
	}
	ll l=0,r=1e15;
	while(l<=r)
	{
		ll mid=(l+r)>>1;
		if(check(mid))r=mid-1;
		else l=mid+1;
	}
	for(int i=1;i<=n;i++)l+=b[i];
	printf("%lld\n",l);
	return 0;
}