TRAFFICN - Traffic Network


Đọc đề đẹp hơn ở:
https://codeforces.com/group/FLVn1Sc504/contest/274566/problem/N

The city traffic network consists of n nodes numbered from 1 to n and m one-way 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 two-way roads are proposed as candidates to be constructed. Your task is to write a program to choose one two-way 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 one-way 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 two-way 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 two-way 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


hide comments
utkarsh_bansal: 2020-08-01 13:22:51

it is atmost one two-way road

einsdurchnull: 2020-07-13 18:34:47

Thank you, it was fun

sarthak_19: 2020-07-10 15:43:14

Nice ques on dijkstra

hellboy41: 2020-06-26 19:36:32

getting TLE while using dijkstra with priority queue k (number of two-way edges) times

pumping_iron: 2020-05-26 07:45:25

nice application of dijkstra, though a easy question

Last edit: 2020-05-26 07:45:38

Added by:Jimmy
Date:2009-01-04
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Regional, HCMC 2008 Tic Tac Toe