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<cstdio>
#include<vector>
#include<algorithm>
using i64=long long;
const int N=100007;
int a[N],b[N],p[N],fa[N],vis[N];i64 f[N],sum[N];
std::vector<int>e[N];
int read(){int x;scanf("%d",&x);return x;}
int find(int x){return x==fa[x]? x:fa[x]=find(fa[x]);}
int main ()
{
    int n=read(),m=read();
    for(int i=1;i<=n;++i) a[i]=read(),b[i]=read(),a[i]=std::max(a[i]-b[i],0),p[i]=fa[i]=i;
    std::sort(p+1,p+n+1,[](int i,int j){return a[i]<a[j];});
    for(int i=1,u,v;i<=m;++i) u=read(),v=read(),e[u].push_back(v),e[v].push_back(u);
    for(int i=1;i<=n;++i)
    {
	std::vector<int>son;int u=p[i];
        vis[u]=1,sum[u]=b[u]; 
        for(int v:e[u]) if(vis[v]&&find(u)^find(v)) son.push_back(fa[v]),sum[u]+=sum[fa[v]],fa[fa[v]]=u;
        f[u]=sum[u]+a[u];
        for(int v:son) f[u]=std::min(f[u],sum[u]-sum[v]+std::max((i64)a[u],f[v])); 
    }
    printf("%lld\n",f[p[n]]);
} 
