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 <cstdio>
#include <algorithm>
#include <vector>
#define file(x) freopen(#x".in", "r", stdin), freopen(#x".out", "w", stdout)

inline int read()
{
	int data = 0, w = 1; char ch = getchar();
	while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
	if (ch == '-') w = -1, ch = getchar();
	while (ch >= '0' && ch <= '9') data = data * 10 + (ch ^ 48), ch = getchar();
	return data * w;
}

const int N(1e5 + 10); const long long INF(1e16);
template <typename T> inline void chkmin(T &x, const T &y) { if (x > y) x = y; }
int n, m, id[N], rnk[N], fa[N];
long long f[N], sum[N], a[N], b[N], c[N];
std::vector<int> G[N], T[N];
int cmp(int x, int y) { return c[x] < c[y]; }
int find(int x) { return fa[x] == x ? x : fa[x] = find(fa[x]); }
void dfs(int x)
{
	sum[x] = b[x], f[x] = INF;
	if (T[x].empty()) return (void) (f[x] = b[x] + c[x]);
	for (auto i : T[x]) dfs(i), sum[x] += sum[i];
	for (auto i : T[x]) chkmin(f[x], sum[x] - sum[i] + std::max(c[x], f[i]));
}

int main()
{
	n = read(), m = read();
	for (int i = 1; i <= n; i++) fa[i] = id[i] = i;
	for (int i = 1; i <= n; i++)
		a[i] = read(), b[i] = read(), c[i] = std::max(a[i] - b[i], 0ll);
	for (int i = 1, x, y; i <= m; i++)
		x = read(), y = read(), G[x].push_back(y), G[y].push_back(x);
	std::sort(id + 1, id + n + 1, cmp);
	for (int i = 1; i <= n; i++) rnk[id[i]] = i;
	for (int i = 1, t; i <= n; i++) for (auto j : G[id[i]])
		if ((t = find(j)) != id[i] && rnk[j] < i)
			fa[t] = id[i], T[id[i]].push_back(t);
	dfs(id[n]); printf("%lld\n", f[id[n]]);
	return 0;
}
