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Contest: Task: Related: TaskD TaskF

Score : $500$ points

Problem Statement

In Takahashi Kingdom, there are $N$ towns, called Town $1$ through Town $N$.
There are also $M$ roads in the kingdom, called Road $1$ through Road $M$. By traversing Road $i$, you can travel from Town $X_i$ to Town $Y_i$, but not vice versa. Here, it is guaranteed that $X_i < Y_i$.
Gold is actively traded in this kingdom. At Town $i$, you can buy or sell $1$ kilogram of gold for $A_i$ yen (the currency of Japan).

Takahashi, a traveling salesman, plans to buy $1$ kilogram of gold at some town, traverse one or more roads, and sell $1$ kilogram of gold at another town.
Find the maximum possible profit (that is, the selling price minus the buying price) in this plan.

Constraints

  • $2 \le N \le 2 \times 10^5$
  • $1 \le M \le 2 \times 10^5$
  • $1 \le A_i \le 10^9$
  • $1 \le X_i \lt Y_i \le N$
  • $(X_i, Y_i) \neq (X_j, Y_j) (i \neq j)$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $A_2$ $A_3$ $\dots$ $A_N$
$X_1$ $Y_1$
$X_2$ $Y_2$
$X_3$ $Y_3$
$\hspace{15pt} \vdots$
$X_M$ $Y_M$

Output

Print the answer.

Sample Input 1

4 3
2 3 1 5
2 4
1 2
1 3

Sample Output 1

3

We can achieve the profit of $3$ yen, as follows:

  • At Town $1$, buy one kilogram of gold for $2$ yen.
  • Traverse Road $2$ to get to Town $2$.
  • Traverse Road $1$ to get to Town $4$.
  • At Town $4$, sell one kilogram of gold for $5$ yen.

Sample Input 2

5 5
13 8 3 15 18
2 4
1 2
4 5
2 3
1 3

Sample Output 2

10

We can achieve the profit of $10$ yen, as follows:

  • At Town $2$, buy one kilogram of gold for $8$ yen.
  • Traverse Road $1$ to get to Town $4$.
  • Traverse Road $3$ to get to Town $5$.
  • At Town $5$, sell one kilogram of gold for $18$ yen.

Sample Input 3

3 1
1 100 1
2 3

Sample Output 3

-99

Note that we cannot sell gold at the town where we bought the gold, which means the answer may be negative.