Dwarf Tower

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 $1$.

Input

The first line contains two integers $n$ and $m(1\le n\le 10^4,0\le m\le 10^5)$ — the number of different items and the number of crafting types.

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

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

Output

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

Examples