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"
using namespace std;
typedef long long ll;
const ll INF = 1LL << 60;
ll A[100000], B[100000], C[100000];
ll sumB[100000];
ll dp[100000];
bool used[100000];
vector<int> G[100000];
struct UnionFind {
	vector<int> par;

	UnionFind(int n) {
		par = vector<int>(n);
		for (int i = 0; i < n; i++) par[i] = i;
	}

	int find(int x) {
		if (x == par[x]) return x;
		return par[x] = find(par[x]);
	}

	bool same(int x, int y) {
		return find(x) == find(y);
	}

	void unite(int x, int y) { // x->y
		x = find(x);
		y = find(y);
		if (x == y) return;
		par[x] = y;
	}
};
bool cmp(int i, int j) {
	return C[i] < C[j];
}
int main() {
	int N, M;
	cin >> N >> M;
	for (int i = 0; i < N; i++) {
		cin >> A[i] >> B[i];
		C[i] = max(A[i] - B[i], 0LL);
	}
	for (int i = 0; i < M; i++) {
		int u, v;
		cin >> u >> v;
		u--; v--;
		G[u].push_back(v);
		G[v].push_back(u);
	}
	vector<int> ord(N);
	iota(ord.begin(), ord.end(), 0);
	sort(ord.begin(), ord.end(), cmp);
	UnionFind U(N);
	for (int i = 0; i < N; i++) {
		int u = ord[i];
		set<int> adj;
		for (int to : G[u]) {
			if (!used[to]) continue;
			adj.insert(U.find(to));
		}
		sumB[u] = B[u];
		for (int v : adj) {
			sumB[u] += sumB[v];
			U.unite(v, u);
		}
		dp[u] = C[u] + sumB[u];
		for (int v : adj) {
			dp[u] = min(dp[u], max(dp[v], C[u]) + sumB[u] - sumB[v]);
		}
		used[u] = 1;
	}
	cout << dp[U.find(0)] << endl;
}