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	<iostream>
#include	<vector>
#include	<sstream>
#include	<iomanip>
#include	<algorithm>

using namespace std;

#define	MaxN 100000

long	A[ MaxN ];
long	B[ MaxN ];
long	C[ MaxN ];
int		P[ MaxN ];
long	F[ MaxN ];
long	S[ MaxN ];
vector< int >	wEdges[ MaxN ];

int
Get( int x ) {
    return ( x == P[ x ] ) ? x : P[ x ] = Get( P[ x ] );
}

void
Main() {
	int	N;	cin >> N;
	int	M;	cin >> M;

	int	wSortedIndex[ MaxN ];
	for ( auto i = 0; i < N; i++ ) {
        cin >> A[ i ] >> B[ i ];
        C[ i ] = max( A[ i ] - B[ i ], long( 0 ) );
        wSortedIndex[ i ] = i;
        P[ i ] = i;
        S[ i ] = B[ i ];
        F[ i ] = C[ i ];
    }
    auto	wRoot = distance( C, max_element( C, C+ N ) );

	for ( auto i = 0; i < M; i++ ) {
		int	wU;	cin >> wU;	wU--;
		int	wV;	cin >> wV;	wV--;
		wEdges[ wU ].emplace_back( wV );
		wEdges[ wV ].emplace_back( wU );
	}
	
    sort( wSortedIndex, wSortedIndex + N, []( int l, int r ) { return C[ l ] < C[ r ]; } );
	
	vector< bool >	wVisited( N, false );

    for ( auto i = 0; i < N; i++ ) {
        int u = wSortedIndex[ i ];
        wVisited[ u ] = true;
        for ( auto v : wEdges[ u ] ) {
        	if ( wVisited[ v ] ) {
				int x = Get( u );
				int	y = Get( v );
				if ( x == y ) continue;
				P[ y ] = x; S[ x ] += S[ y ];
				F[ x ] = min( F[ x ], max( C[ u ] - S[ y ], F[ y ] ) );
            }
        }
    }
    cout << F[ wRoot ] + S[ wRoot ] << endl;
}

int
main() {
	Main();
	return 0;
}
