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>
using namespace std;
#define int long long
const int MAXN=100100;
vector<int> arrive[MAXN];
int a[MAXN],b[MAXN],p[MAXN];
int fa[MAXN];
int f[MAXN],s[MAXN],vis[MAXN];
int n,m;
inline int find(register int x)
{
	return fa[x]==x?x:fa[x]=find(fa[x]);
}
inline void Addedge(register int u,register int v)
{
	arrive[u].push_back(v);
	return;
}
inline bool cmp_(register int x,register int y)
{
	return a[x]<a[y];
}
signed main()
{
	ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
	cin>>n>>m;
	for(register int i=1;i<=n;i++) cin>>a[i]>>b[i],a[i]=max(a[i]-b[i],0LL),p[i]=fa[i]=i;
	sort(p+1,p+n+1,cmp_);
	for(register int i=1,x,y;i<=m;i++) cin>>x>>y,Addedge(x,y),Addedge(y,x);
	for(register int i=1;i<=n;i++)
	{
		vector<int> sonnow;
		register int now=p[i];
		vis[now]=1,s[now]=b[now];
		for(register int i=0;i<(int)arrive[now].size();i++)
		{
			register int val=arrive[now][i];
			if((!vis[val])||find(now)==find(val)) continue;
			sonnow.push_back(find(val));
			s[now]+=s[find(val)];
			fa[find(val)]=now;
		}
		f[now]=s[now]+a[now];
		for(register int i=0;i<(int)sonnow.size();i++) f[now]=min(f[now],s[now]-s[sonnow[i]]+max(a[now],f[sonnow[i]]));
	}
	cout<<f[p[n]]<<endl;
	return 0;
}