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 int long long
using namespace std;
const int maxn=100007;
int a[maxn],n,m,f[maxn],vis[maxn],sum[maxn],b[maxn],c[maxn],p[maxn],fa[maxn];
vector<int>v[maxn];
int find(int x){return fa[x]==x?fa[x]:fa[x]=find(fa[x]);}
inline bool cmp(int x,int y){return c[x]<c[y];}
signed main(){
	cin>>n>>m;
	for(int i=1;i<=n;++i)cin>>a[i]>>b[i],p[i]=fa[i]=i,c[i]=max(a[i]-b[i],0ll);
	sort(p+1,p+1+n,cmp);
	for(int i=1,x,y;i<=m;++i){
		cin>>x>>y;v[x].push_back(y);v[y].push_back(x);
	}
	for(int i=1;i<=n;++i){
		int x=p[i];vis[x]=1;
		sum[x]=b[x];vector<int>son;
		for(auto y:v[x])if(find(y)^find(x)&&vis[y])sum[x]+=sum[find(y)],son.push_back(find(y)),fa[find(y)]=find(x);
		f[x]=sum[x]-b[x]+max(a[x],b[x]);
		for(auto y:son)f[x]=min(f[x],sum[x]-b[x]-sum[y]+max(max(a[x],b[x]),f[y]+b[x]));
	}
	cout<<f[p[n]];
}