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 int long long
using namespace std;
int n, m, a[100007], b[100007], c[100007], l[100007], f[100007], dp[100007], sum[100007];
vector<int>e[100007], s[100007];
bool vis[100007];
int read()
{
	int num = 0;
	char c = getchar();
	while (c < '0' || c>'9')c = getchar();
	while (c >= '0' && c <= '9')num = num * 10 + c - '0', c = getchar();
	return num;
}
int cmp(int a, int b)
{
	return c[a] < c[b];
}
int find(int x)
{
	if (f[x] == x)return x;
	return f[x] = find(f[x]);
}
int dfs(int w)
{
	sum[w] = b[w];
	for (int i = 0, lim = s[w].size(); i < lim; i++)
		dfs(s[w][i]), sum[w] += sum[s[w][i]];
	dp[w] = sum[w] + c[w];
	for (int i = 0, lim = s[w].size(); i < lim; i++)
		dp[w] = min(dp[w], sum[w] - sum[s[w][i]] + max(c[w], dp[s[w][i]]));
	return 0;
}
signed main()
{
	n = read();
	m = read();
	for (int i = 1; i <= n; i++)
	{
		a[i] = read();
		b[i] = read();
		c[i] = max(a[i] - b[i], 0LL);
		l[i] = f[i] = i;
	}
	for (int i = 1; i <= m; i++)
	{
		int a = read(), b = read();
		e[a].push_back(b);
		e[b].push_back(a);
	}
	sort(l + 1, l + n + 1, cmp);
	for (int i = 1; i <= n; i++)
	{
		int x = l[i];
		vis[x] = 1;
		for (int j = 0, lim = e[x].size(); j < lim; j++)
			if (x != find(e[x][j]) && vis[e[x][j]])
				s[x].push_back(find(e[x][j])), f[find(e[x][j])] = x;
	}
	dfs(l[n]);
	cout << dp[l[n]] << endl;
	return 0;
}