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 int maxn = 100010;

int n, m, l[maxn], e = 0;

int A[maxn], B[maxn], C[maxn], ind[maxn], vis[maxn];
ll val[maxn], sum[maxn];

struct Edge {
	int v, x;
} E[maxn << 1];

inline void addEdge(int u, int v) {
	E[e].v = v; E[e].x = l[u]; l[u] = e++;
}

int fa[maxn];

int getroot(int x) {
	if (x == fa[x]) return x;
	return fa[x] = getroot(fa[x]);
}

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

int main() {
	memset(l, -1, sizeof(l));
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i++) scanf("%d%d", &A[i], &B[i]);
	for (int i = 1; i <= m; i++) {
		int u, v; scanf("%d%d", &u, &v);
		addEdge(u, v); addEdge(v, u);
	}
	for (int i = 1; i <= n; i++) fa[i] = ind[i] = i, C[i] = max(A[i] - B[i], 0), sum[i] = B[i];
	sort(ind+1, ind+n+1, cmp);
	for (int _ = 1; _ <= n; _++) {
		vector<int> vec;
		int i = ind[_];
		vis[i] = 1;
		for (int p = l[i]; p >= 0; p = E[p].x) if (vis[E[p].v]) vec.push_back(getroot(E[p].v));
		sort(vec.begin(), vec.end()); vec.erase(unique(vec.begin(), vec.end()), vec.end());
		val[i] = C[i];
		for (int x = 0; x < vec.size(); x++) {
			int v = vec[x];
			// sum[v] + ? >= C[i]
			// ? >= C[i] - sum[v];
			// ? >= val[v]
			val[i] = min(val[i], max(C[i] - sum[v], val[v]));
			fa[v] = i; sum[i] += sum[v];
		}
	}
	printf("%lld\n", val[getroot(1)]+sum[getroot(1)]);
	return 0;
}