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 <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#define MAXN 100010

int n, m, a[MAXN], b[MAXN], c[MAXN], p[MAXN];
struct edge {
    int u, v, w;
    inline friend bool operator<(const edge &a, const edge &b) {
        return a.w < b.w;
    }
} e[MAXN];
inline int find(int x) { return x == p[x] ? x : p[x] = find(p[x]); }
std::vector<int> next[MAXN];
long long sum[MAXN];

long long dp(int x) {
    long long ret = c[x];
    sum[x] = b[x];
    for (int y : next[x]) {
        long long res = dp(y);
        ret = std::min(ret, std::max(0LL + c[x], res) - sum[y]);
        sum[x] += sum[y];
    }
    return ret + sum[x];
}

int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) {
        scanf("%d%d", &a[i], &b[i]);
        a[i] = std::max(a[i], b[i]);
        c[i] = a[i] - b[i];
        p[i] = i;
    }
    for (int i = 1; i <= m; i++) {
        scanf("%d%d", &e[i].u, &e[i].v);
        e[i].w = std::max(c[e[i].u], c[e[i].v]);
    }
    std::sort(e + 1, e + m + 1);
    for (int i = 1; i <= m; i++) {
        int u = e[i].u, v = e[i].v;
        if (find(u) == find(v)) continue;
        if (c[u] < c[v]) std::swap(u, v);
        next[find(u)].push_back(find(v));
        p[find(v)] = find(u);
    }
    printf("%lld\n", dp(find(1)));
    return 0;
}