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 <iostream>
#include <cstdlib>
#include <cmath>
#include <string>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <set>
#include <map>
#define re register
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
#define MAXN 100507
#define mo 19930726
#define ll long long
using namespace std;
typedef unsigned long long ull;
#define ms(arr) memset(arr, 0, sizeof(arr))
const int inf = 0x3f3f3f3f;
int head[MAXN],fa[MAXN],a[MAXN],b[MAXN],c[MAXN],n,m,vis[MAXN],id[MAXN],cnt,num;
ll s[MAXN],f[MAXN];
struct po{
	int nxt,to;
}edge[MAXN<<1];
vector<int> v[MAXN];
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
inline bool cmp(int x,int y) {return c[x]<c[y];}
inline void add_edge(int from,int to){
	edge[++num].nxt=head[from];edge[num].to=to;head[from]=num;
}
void dfs(int u){
	s[u]=b[u];
	for(int i=head[u];i;i=edge[i].nxt){
		int v=edge[i].to;
		dfs(v);
		s[u]+=s[v];
	}
	f[u]=s[u]+c[u];
	for(int i=head[u];i;i=edge[i].nxt){
		int v=edge[i].to;
		f[u]=min(f[u],s[u]-s[v]+max(f[v],1ll*c[u]));
	}
}
int main()
{
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		cin>>a[i]>>b[i];
		c[i]=max(0,a[i]-b[i]);
		fa[i]=id[i]=i;
	}
	for(int i=1;i<=m;i++){
		int x,y;
		cin>>x>>y;
		v[x].push_back(y); v[y].push_back(x);
	}
	sort(id+1,id+n+1,cmp);
	for(int i=1;i<=n;i++){
		int x=id[i];vis[x]=1;
		for(int j=0;j<v[x].size();j++) {
			int y=v[x][j];
			if(!vis[y]) continue;
			y=find(y);
			if(x!=y){
				fa[y]=x;add_edge(x,y);
			}
		}
	}
	dfs(id[n]);
	cout<<f[id[n]];
}