题目描述

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 $c_i$ 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 $1$ .

输入格式

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

The second line contains $n$ integers $c_i -$ values of the items $(0 \le c_i \le 10^9)$ .

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 $y_i (1 \le a_i, x_i, y_i \le n , a_i \ne x_i, x_i \ne y_i, y_i \ne a_i)$.

输出格式

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

5 3
5 0 1 2 5
5 2 3
4 2 3
1 4 5

2

提示

Time limit: 2 s, Memory limit: 256 MB.