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.