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
#define N 100010
#define pb emplace_back
using namespace std;
vector<int> e[N];
int m,n,w[N],x,y,f[N];
ll a[N],b[N],sb[N],dp[N];
void jb(int x,int y){e[x].pb(y);}
bool xi(int x,int y){return (a[x]-b[x]<a[y]-b[y])||(a[x]-b[x]==a[y]-b[y]&&x<y);}
bool c1(const int &x,const int &y){return xi(x,y);}
int quef(int x){if (f[x]!=x) f[x]=quef(f[x]);return f[x];}
void lb(int x,int y){
	if (x==y)return ;f[y]=x;
	sb[x]+=sb[y];dp[x]=min(dp[x],max(dp[y],a[x]-b[x])-sb[y]);
}
int main(){
	cin>>n>>m;
	for (int i=1;i<=n;i++){cin>>a[i]>>b[i];w[i]=f[i]=i;}
	for (int i=1;i<=m;i++){cin>>x>>y;jb(x,y);jb(y,x);}
	sort(w+1,w+n+1,c1);
	for (int i=1;i<=n;i++){
		dp[w[i]]=max(0ll,a[w[i]]-b[w[i]]),sb[w[i]]=b[w[i]];
		for (auto j:e[w[i]]){
			if (xi(j,w[i]))lb(w[i],quef(j));
		}
		dp[w[i]]+=sb[w[i]];
	}
	cout<<dp[w[n]]<<endl;
	return 0;
}