A game has ~n~ rooms and ~m~ tunnels between them. Each room has a certain number of coins. What is the maximum number of coins you can collect while moving through the tunnels when you can freely choose your starting and ending room?

Input

• The first input line has two integers ~n~ and ~m~: the number of rooms and tunnels. The rooms are numbered ~1,2,\dots,n~.

Then, there are ~n~ integers ~k\_1,k\_2,\ldots,k\_n~: the number of coins in each room.

Finally, there are ~m~ lines describing the tunnels. Each line has two integers ~a~ and ~b~: there is a tunnel from room ~a~ to room ~b~. Each tunnel is a one-way tunnel.

Output

• Print one integer: the maximum number of coins you can collect.

Constraints

• ~1 \le n \le 10^5~
• ~1 \le m \le 2 \cdot 10^5~
• ~1 \le k\_i \le 10^9~
• ~1 \le a,b \le n~

Example Input

4 4
4 5 2 7
1 2
2 1
1 3
2 4

Example Output

16