Little Vasya is playing a new game named "Dwarf Tower". In this game there are n different items, which you can put on your dwarf character. Items are numbered from 1 to n. Vasya wants to get the item with number 1.

There are two ways to obtain an item:

• You can buy an item. The i-th item costs ci money.
• You can craft an item. This game supports only m types of crafting. To craft an item, you give two particular different items and get another one as a result.

Help Vasya to spend the least amount of money to get the item number 1.

Input

The first line contains two integers n and m (1 ≤ n ≤ 10000, 0 ≤ m ≤ 100000) - the number of different items and the number of crafting types.

The second line contains n integers ci - values of the items (0 ≤ ci ≤ 109).

The following m lines describe crafting types, each line contains three distinct integers ai, xi, yi - ai is the item that can be crafted from items xi and yi (1 ≤ ai, xi, yi ≤ n, ai ≠ xi, xi ≠ yi, yi ≠ ai).

Output

Print a single integer - the least amount of money to spend.