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 F(i,a,b) for(int i=(a);i<=(b);++i)
#define F_(i,a,b) for(int i=(a);i>=(b);--i)
#define G(i,u) for(int i=head[u];i;i=nxt[i])
 
typedef long long ll;
 
const int N = 100005;
 
template<typename T> inline T min(T& a, T b) {return a<b?a:a=b;}
 
int head[N], to[N<<1], nxt[N<<1], a[N], b[N], r[N], g[N], son[N], ecnt;
void add(int u, int v) { to[++ecnt] = v; nxt[ecnt] = head[u]; head[u] = ecnt; }
bool cmp(const int& x, const int& y) { return a[x] < a[y]; }
int find(int x) { return g[x] == x? x: g[x] = find(g[x]); }
ll f[N], sum[N];
int main() {
	int n, m;
	scanf("%d%d", &n, &m);
	F(i,1,n) {
		scanf("%d%d", &a[i], &b[i]);
		a[i] = std::max(a[i]-b[i],0); 
		r[i] = i;
	}
	F(i,1,m) {
		int u, v;
		scanf("%d%d", &u, &v);
		add(u,v); add(v,u);
	}
	std::sort(r+1,r+n+1,cmp);
	F(i,1,n) {
		int x = r[i], tot = 0; g[x] = x; sum[x] = b[x];
		G(j,x) {
			int v = to[j], p = find(v);
			if(!p || p == x) continue;
			son[++tot] = p;
			sum[x] += sum[p];
			g[p] = x;
		}
		f[x] = a[x] + sum[x];
		F(j,1,tot) min(f[x],sum[x]-sum[son[j]]+std::max(f[son[j]],1ll*a[x]));
	}
	printf("%lld\n", f[r[n]]);
	return 0;
} 