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>
typedef long long ll ;
#define rep(i, a, b) for (int i = a; i <= b; ++i)
using namespace std;

template <typename tn> void read (tn & a) {
	tn x = 0, f = 1; char c = getchar();
	while (c < '0' || c > '9'){ if (c == '-') f = -1; c = getchar(); }
	while (c >= '0' && c <= '9'){ x = x * 10 + c - '0'; c = getchar(); }
	a = f == 1 ? x : -x;
}

const int MAXN = 100100;
const int Ln = 22;
const int INF = 2e9;
ll n, m;
ll a[MAXN], b[MAXN];
vector<int> g[MAXN];
ll f[MAXN], fa[MAXN], bsum[MAXN], p[MAXN];
bool vis[MAXN];

ll find (int x) { return fa[x] == 0 || fa[x] == x ? x : fa[x] = find(fa[x]); }
bool cmp (int i, int j) { return a[i] < a[j]; }

int main() {
	read(n);
	read(m);
	rep(i, 1, n) read(a[i]), read(b[i]);
	rep(i, 1, m) {
		int u, v;
		read(u);
		read(v);
		g[u].push_back(v);
		g[v].push_back(u);
	}
	rep(i, 1, n) {
		a[i] -= b[i];
		if (a[i] < 0) a[i] = 0;
		fa[i] = i;
		p[i] = i;
		vis[i] = 0;
	}
	sort(p + 1, p + 1 + n, cmp);
	rep(i, 1, n) {
		int x = p[i];
		f[x] = a[x];
		bsum[x] = b[x]; 
		vis[x] = 1;
		rep(j, 0, (int) g[x].size() - 1) {
			int v = g[x][j];
			if (vis[v]) {
				int y = find(v);
				if (x != y) {
//					cerr<<"   "<<y<<"\n";
					fa[y] = x;
					bsum[x] += bsum[y];
					f[x] = min(f[x], max(f[y], a[x] - bsum[y]) );
				}
			}
		}
//          cerr<<i<<" "<<x<<" "<<f[x]<<"\n";
	}
	cout << f[p[n]] + bsum[p[n]]<<"\n";
	return 0;
}
