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 ld double
#define ull unsigned long long
#define ll long long
#define pii pair <int, int>
#define iiii pair <int, pii>
#define mp make_pair
#define INF 1000000000
#define MOD 1000000007
#define rep(i, x) for(int (i) = 0; (i) < (x); (i)++)
inline int getint() {
  int x = 0, p = 1; char c = getchar();	
  while (c <= 32) c = getchar();
  if (c == 45) p = -p, c = getchar();
  while (c > 32) x = x * 10 + c - 48, c = getchar();
  return x * p;
}
using namespace std;
//ruogu_alter
const int N = 1e5 + 5;
int n, m, a[N], b[N], c[N], id[N], par[N];
ll f[N], s[N];
bool vis[N];
vector<int> g[N];
//
int findset(int x) {
  return par[x] == x ? x : par[x] = findset(par[x]);
}
bool cmp(int x, int y) {
  return a[x] < a[y];
}
int main() {
  n = getint(); m = getint();
  rep(i, n) {
    a[i] = getint(), b[i] = getint();
    a[i] = max(a[i] - b[i], 0);
    par[i] = id[i] = i;
    f[i] = a[i] + b[i]; s[i] = b[i];
  }
  rep(i, m) {
    int x = getint() - 1, y = getint() - 1;
    g[x].emplace_back(y);
    g[y].emplace_back(x);
  }
  sort(id, id + n, cmp);
  rep(ii, n) {
    int x = id[ii]; vis[x] = true;
    rep(i, g[x].size()) {
      int to = findset(g[x][i]);
      if (!vis[to] || to == x) continue;
      f[x] = min(f[x] + s[to], s[x] + max(f[to], 1ll * a[x]));
      s[x] += s[to]; par[to] = x;
    }
  }
  cout << f[findset(0)] << endl;
  return 0;
}
