Problem Statement

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.