Donation

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

inputFormat

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

outputFormat

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

样例

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

44