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 fo(i, x, y) for(int i = x, B = y; i <= B; i ++)
#define ff(i, x, y) for(int i = x, B = y; i <  B; i ++)
#define fd(i, x, y) for(int i = x, B = y; i >= B; i --)
#define ll long long
#define pp printf
#define hh pp("\n")
using namespace std;

const int N = 1e5 + 5;

int n, m, x, y;
int a[N], b[N];
int f[N], d[N], nd[N];
int F(int x) {
	return f[x] == x ? x : (f[x] = F(f[x]));
}

#define V vector<int>
#define pb push_back
#define si size()
V e[N];

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

ll sumb[N], g[N];

int main() {
	scanf("%d %d", &n, &m);
	fo(i, 1, n) scanf("%d %d", &a[i], &b[i]), a[i] = max(0, a[i] - b[i]);
	fo(i, 1, m) {
		scanf("%d %d", &x, &y);
		e[x].pb(y); e[y].pb(x);
	}
	fo(i, 1, n) f[i] = i, sumb[i] = b[i], g[i] = a[i];
	fo(i, 1, n) d[i] = i;
	sort(d + 1, d + n + 1, cmp);
	fo(i, 1, n) nd[d[i]] = i;
	fo(i, 1, n) {
		int x = d[i];
		ff(j, 0, e[x].si) {
			int y = e[x][j];
			if(nd[y] > nd[x]) continue;
			if(F(x) != F(y)) {
				int u = f[x], v = f[y];
				f[v] = u;
				sumb[u] += sumb[v];
				g[u] = min(g[u], max(g[v], a[u] - sumb[v]));
			} 
		}
	}
	int x = F(d[n]);
	pp("%lld\n", g[x] + sumb[x]);
}
