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 fi first
#define se second
#ifdef CX_TEST
#define Debug printf
#else
#define Debug(...)
#endif
#define LL long long
using namespace std;
typedef pair<int, int> P;
const int maxn = 1e5 + 5;

int a[maxn], b[maxn], c[maxn], p[maxn];
LL s[maxn], d[maxn];
bool vis[maxn];
vector<int> g[maxn];

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

int ff(int x) {
    if(p[x] != x) p[x] = ff(p[x]);
    return p[x];
}

int main() {
#ifdef CX_TEST
    freopen("E:\\program--GG\\test_in.txt", "r", stdin);
#endif
    int n, m, i, j, u, v;
    scanf("%d%d", &n, &m);
    for(i = 1;i <= n; i++) {
        scanf("%d%d", &a[i], &b[i]);
        a[i] = max(a[i] - b[i], 0);
        s[i] = b[i];
        d[i] = a[i];
    }
    for(i = 0;i < m; i++) {
        scanf("%d%d", &u, &v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
    for(i = 1;i <= n; i++) c[i] = i;
    for(i = 1;i <= n; i++) p[i] = i;
    sort(c + 1, c + n + 1, cmp);
    for(i = 1;i <= n; i++) {
        j = c[i];
        vis[j] = 1;
        for(auto e:g[j]) {
            if(vis[e]) {
                u = ff(j), v = ff(e);
                if(u != v) {
                    s[u] += s[v];
                    p[v] = u;
                    d[u] = min(d[u], d[v] + max(0LL, a[u] - d[v] - s[v]));
                }
            }
        }
    }
    cout << s[c[n]] + d[c[n]] << endl;
    return 0;
}
