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 fir first
#define sec second
#define db double
#define ll long long
#define ev eg[i].v
#define pb push_back
#define INF 1000000007
#define pir pair<int,int>
#define Rep(i,l,r) for(int i=(l);i<=(r);++i)
#define RepD(i,r,l) for(int i=(r);i>=(l);--i)
#define RepG(i,x) for(int i=hd[x];i;i=eg[i].nxt)
using namespace std;

const int N=1e5+5;

ll hd[N],cnt=0;bool vis[N];
struct Eg{ll v,nxt;}eg[N*2];
ll a[N],b[N],c[N],fa[N],f[N],g[N];

ll find(ll x){return fa[x]==x?x:fa[x]=find(fa[x]);}
void add(ll u,ll v){eg[++cnt]=(Eg){v,hd[u]},hd[u]=cnt;}

bool cmp(ll x,ll y){return a[x]<a[y];}

int main(){
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	ll n,m;
	scanf("%lld%lld",&n,&m);
	Rep(i,1,n) scanf("%lld%lld",&a[i],&b[i]),a[i]=max(a[i]-b[i],0ll);
	Rep(i,1,m){
		ll u,v;
		scanf("%lld%lld",&u,&v);
		add(u,v),add(v,u);	
	}
	Rep(i,1,n) c[i]=fa[i]=i;
	sort(c+1,c+n+1,cmp);
	Rep(k,1,n){
		ll x=c[k];
		vis[x]=1,f[x]=a[x],g[x]=b[x];
		RepG(i,x)
			if(vis[ev]){
				ll ff=find(ev);
				if(x==ff) continue;
				fa[ff]=x,g[x]+=g[ff];
				f[x]=min(f[x],max(f[ff],a[x]-g[ff]));	
			}
	}
	printf("%lld\n",f[c[n]]+g[c[n]]);
	return 0;
}


