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.