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<cstring>
#include<cstdio>
#include<cstring>
#include<vector>
#include<queue>
#include<algorithm>
#include<climits>
#include<bitset>
#define pii pair<int,int>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define int long long
using namespace std;
inline int read(){
    int f=1,ans=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){ans=ans*10+c-'0';c=getchar();}
    return f*ans;
}
const int MAXN=1e5+11;
vector<int> vec[MAXN],vec1[MAXN];
int N,M,f[MAXN],vis[MAXN],A[MAXN],B[MAXN],C[MAXN],S[MAXN],p[MAXN];
struct Union{
    int f[MAXN];void init(){for(int i=1;i<=N;i++) f[i]=i;return;}
    int find(int x){return f[x]==x?x:f[x]=find(f[x]);}
}SS;
bool cmp(int x,int y){return C[x]<C[y];}
void dfs(int u){
    S[u]=B[u];for(auto v:vec[u]){dfs(v),S[u]+=S[v];}
    f[u]=S[u]+C[u];for(auto v:vec[u]) f[u]=min(f[u],S[u]-S[v]+max(f[v],C[u]));
    return;
}
signed main(){
    N=read(),M=read();for(int i=1;i<=N;i++) A[i]=read(),B[i]=read(),C[i]=max(A[i]-B[i],0ll),p[i]=i;
    for(int i=1;i<=M;i++){int u=read(),v=read();vec1[u].pb(v),vec1[v].pb(u);}SS.init();
    sort(p+1,p+N+1,cmp);
    for(int i=1;i<=N;i++){
        int u=p[i];
        for(auto v:vec1[u]) if(vis[v]&&SS.find(v)!=u) {vec[u].pb(SS.find(v)),SS.f[SS.find(v)]=u;}vis[u]=1;
    }dfs(p[N]);printf("%lld\n",f[p[N]]);return 0;
}

