Transport Goods

Time Limit: 2 Seconds
Memory Limit: 65536 KB

The HERO country is attacked by other country. The intruder is attacking the
capital so other cities must send supports to the capital. There are some roads
between the cities and the goods must be transported along the roads.

According the length of a road and the weight of the goods, there will be some
cost during transporting. The cost rate of each road is the ratio of the cost
to the weight of the goods transporting on the road. It is guaranteed that the
cost rate is less than 1.

On the other hand, every city must wait till all the goods arrive, and then
transport the arriving goods together with its own goods to the next city. One
city can only transport the goods to one city.

Your task is find the maximum weight of goods which can arrive at the capital.

Input

There are several cases.

For each case, there are two integers N (2 <= N <= 100) and M in the first
line, where N is the number of cities including the capital (the capital is
marked by N, and the other cities are marked from 1 to N-1), and M is the number
of roads.

Then N-1 lines follow. The i-th (1 <= i <= N - 1) line contains a positive
integer (<= 5000) which represents the weight of goods which the i-th city
will transport to the capital.

The following M lines represent M roads. There are three numbers A, B, and C
in each line which represent that there is a road between city A and city B,
and the cost rate of this road is C.

Process to the end of the file.

**Output**

For each case, output in one line the maximum weight which can be transported
to the capital, accurate up to 2 demical places.

**Sample Input**

5 6

10

10

10

10

1 3 0

1 4 0

2 3 0

2 4 0

3 5 0

4 5 0

Sample Output

40.00

*
*

Author:

**ZHANG, Bo**
Source:

**ZOJ Monthly, October 2003**
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