Description

It is the 22^nd century, and machines with supreme artificial intelligence have conquered the world. Humans are kept alive by a computer controlled program, the Matrix, for no other purpose than providing energy to the machines. Only a small group of freedom fighters have escaped the Matrix and built a secret resist base, Zion, near the core of the earth. However the machines have discovered this and send down millions of sentinels to destroy Zion.

The underground world is actually the sewers of the previous cities in ruin — gigantic tunnels connecting the ground, Zion, and various other intersections. However all sewers have been destroyed when the machines first conquered the mankind. Because of limited time, the sewers have been repaired by people from Zion such that there will always be no more than one path from one intersection to another. No tunnel connects an intersection to itself. The best weapon we have is EMP (electromagnetic pulse) charge, an extremely powerful weapon to use against machines. Blowing an EMP charge will cause any electronic device within its range to stop functioning, therefore destroying the machines within range completely. However it can also cause another EMP charge within the range to malfunction, so the distance between any two EMP charges must be no less than their range.

The council has decided to put EMP on certain intersections to minimize the possibility of the machines destroying Zion. Since our resources are limited, we can only afford to put EMP charges on certain intersections of the underground tunnels. Deploying an EMP charge on a certain intersection has a non-negative cost. What is the maximal distance you can cover with EMP charges, and what’s the minimum cost to achieve that maximal distance?

Input

There are multiple test cases in the input file. Each test case starts with three integers N, M and D, (2 ≤ N ≤ 300, 1 ≤ M ≤ 3000), the number of intersections, the number of edges, and the range of each EMP charge, respectively. Intersections are numbered from 0 to N − 1. The following line consists of N integers, the cost of deploying an EMP charge on intersection i. The next M lines each consists of three integers S, T, and C, (0 ≤ S, T ≤ N − 1, 1 ≤ C ≤ 20000), meaning that intersection S and T are connected by a tunnel whose length is C. Every test case ends with one blank line indicating the end of test case.

N = 0, M = 0, D = 0 indicates the end of input file and should not be processed by your system.

Output

For each test case, output two integers in the format as indicated in the sample output: the maximum distance EMPs can cover and the minimum cost you’ve found on a single line.

2 1 3
5 6
1 0 6

0 0 0

Case 1: 6 11

Source

Shanghai 2006