Competitions

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 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 (1n10000, 0m100000) - the number of different items and the number of crafting types.

The second line contains n integers ci - values of the items (0ci109).

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 (1ai, xi, yin, aixi, xiyi, yiai).

Output

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

Time limit 1 second
Memory limit 128 MiB
Input example #1
5 3
5 0 1 2 5
5 2 3
4 2 3
1 4 5

Output example #1
2

Input example #2
3 1
2 2 1
1 2 3

Output example #2
2

Source 2013 ACM NEERC, Northern Subregional Contest, St Petersburg, October 26