TRAFFICN  Traffic Network
English  Vietnamese 
The city traffic network consists of n nodes numbered from 1 to n and m oneway roads connecting pairs of nodes. In order to reduce the length of the shortest path between two different critical nodes s and t, a list of k twoway roads are proposed as candidates to be constructed. Your task is to write a program to choose one twoway road from the proposed list in order to minimize the resulting shortest path between s and t.
Input
The input file consists of several data sets. The first line of the input file contains the number of data sets which is a positive integer and is not bigger than 20. The following lines describe the data sets.
For each data set, the first line contains five positive integers n (n ≤ 10 000), m (m ≤ 100 000), k (k < 300), s (1 ≤ s ≤ n), t (1 ≤ t ≤ n) separated by space. The ith line of the following m lines contains three integers di, ci, li separated by space, representing the length li ( 0< li ≤ 1000) of the ith oneway road connecting node di to ci. The jth line of the next k lines contains three positive integers uj, vj and qj (qj ≤ 1000) separated by space, representing the jth proposed twoway road of length qj connecting node uj to vj.
Output
For each data set, write on one line the smallest possible length of the shortest path after building the chosen one twoway road from the proposed list. In case, there does not exist a path from s to t, write 1.
Example
Sample Input 1 4 5 3 1 4 1 2 13 2 3 19 3 1 25 3 4 17 4 1 18 1 3 23 2 3 5 2 4 25 Sample Output 35
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VAIBHAV TRIVEDI:
20131203 19:10:27
AC keep track of the limit of INF in dist array Last edit: 20140329 05:24:35 

technophyle:
20130729 17:36:18
All those getting WA print 1 and check Neo's note. Indeed a very important condition!!!! 

Panagiotis Kostopanagiotis:
20130108 12:47:55
Last edit: 20130314 18:28:49 

Rocker3011:
20121010 01:38:54
can somebody provide me a tricky test case? all of them seems to work just fine :7 

Pratham Khandelwal:
20100825 11:00:04
You may or may not use one twoway road from the proposed list. 

Lewin Gan:
20100504 21:40:12
I wrote this in Java and got TLE, but rewrote the same exact algorithm in C++ and got AC


Jorge Bernadas:
20091121 19:31:25
@writer: Might you add this case:

Added by:  Duc 
Date:  20090104 
Time limit:  0.140s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ACM Regional, Ho Chi Minh City 2008 