Dwarf Tower

문제

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.

입력

The first line of input contains two integers n and m (1 ≤ n ≤ 10 000; 0 ≤ m ≤ 100 000) — the number of different items and the number of crafting types.

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

The following m lines describe crafting types, each line contains three distinct integers a_i, x_i, y_i — a_i is the item that can be crafted from items x_i and y_i (1 ≤ a_i, x_i, y_i ≤ n, a_i ≠ x_i, x_i ≠ y_i, y_i ≠ a_i).

출력

The output should contain a single integer — the least amount of money to spend.