MICEMAZE - Mice and Maze

A set of laboratory mice is being trained to escape a maze. The maze is made up of cells, and each cell is connected to some other cells. However, there are obstacles in the passage between cells and therefore there is a time penalty to overcome the passage Also, some passages allow mice to go one-way, but not the other way round.

Suppose that all mice are now trained and, when placed in an arbitrary cell in the maze, take a path that leads them to the exit cell in minimum time.

We are going to conduct the following experiment: a mouse is placed in each cell of the maze and a count-down timer is started. When the timer stops we count the number of mice out of the maze.

Problem

Write a program that, given a description of the maze and the time limit, predicts the number of mice that will exit the maze. Assume that there are no bottlenecks is the maze, i.e. that all cells have room for an arbitrary number of mice.

Input

The maze cells are numbered $1, 2, \ldots, N$, where $N$ is the total number of cells. You can assume that $N \le 100$.

The first three input lines contain $N$, the number of cells in the maze, $E$, the number of the exit cell, and the starting value $T$ for the count-down timer (in some arbitrary time unit).

The fourth line contains the number $M$ of connections in the maze, and is followed by $M$ lines, each specifying a connection with three integer numbers: two cell numbers $a$ and $b$ (in the range $1, \ldots, N$) and the number of time units it takes to travel from $a$ to $b$.

Notice that each connection is one-way, i.e., the mice can't travel from $b$ to $a$ unless there is another line specifying that passage. Notice also that the time required to travel in each direction might be different.

Output

The output consists of a single line with the number of mice that reached the exit cell $E$ in at most $T$ time units.

Example

Input:
4 
2 
1
8
1 2 1
1 3 1
2 1 1
2 4 1
3 1 1
3 4 1
4 2 1
4 3 1

Output:
3

Added by:overwise
Date:2007-10-04
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 ICPC -- SWERC 2001

hide comments
2016-11-12 18:30:42
Easy one with dijkstra's :-)
2016-11-10 17:29:10 Sahil
Flloyd Warshall works well here.
2016-09-24 14:50:16
Nice dijkstra problem :D
2016-08-25 19:33:13
any one please help me about constraints..??
2016-07-05 17:59:28
No one ever told me that I can't start a sized array from 1. Costed me 8 runtime error... :( ;(

Last edit: 2016-07-06 09:10:42
2016-06-24 06:03:47 Shubhransh Srivastav
need to clear the vector first... cost me 4 wa!!!
thanks ajay_5097 :)
2016-06-03 15:58:37
If you are using vector then please
before pushing any value in the vector, clear the vector first
It cost me 1 WA...
2016-04-21 23:01:31 Akshay Damle
Nice dijkstra problem for beginners
2016-02-09 15:55:54
can anyone explain the test case>?
2016-02-03 09:18:21
Nice dijkstra's . Do http://www.spoj.com/problems/TRAFFICN/ after this.
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.