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 <cstdio>
# include <algorithm>
using namespace std;
const int N = 3e5 + 12;
const int inf = 0x7fffffff;
int a[N],b[N],id[N],n,m,head[N],dt,fa[N];bool vis[N];
long long f[N],s[N];
int find(int x){return fa[x] == x ? x : fa[x] = find(fa[x]);}
struct Edge{int to,nex;}edge[N << 2];
void AddEdge(int u,int v){edge[++dt] = (Edge){v,head[u]};head[u] = dt;}
bool cmp(int x,int y){return a[x] < a[y];}
int main()
{
	scanf("%d %d",&n,&m);
	for(int i = 1;i <= n;i++)scanf("%d %d",&a[i],&b[i]),a[i] = max(a[i] - b[i],0),id[i] = fa[i] = i;
	sort(id + 1,id + n + 1,cmp);int u,v;
	for(int i = 1;i <= m;i++)scanf("%d %d",&u,&v),AddEdge(u,v),AddEdge(v,u);
	for(int t = 1;t <= n;t++)
	{
		u = id[t];vis[u] = true;f[u] = a[u];s[u] = b[u];
		for(int i = head[u];i;i = edge[i].nex)if(vis[edge[i].to])
		{
			v = find(edge[i].to);
			if(u == v)continue;
			fa[v] = u;s[u] += s[v];
			f[u] = min(f[u],max(f[v],a[u] - s[v])); 
		}
	}
	printf("%lld\n",f[id[n]] + s[id[n]]);
}