The government of Spoj_land has selected number of locations in the city for road construction and numbered those locations as 0,1,2,3,.......500.

Now, they want to construct roads between various pairs of location(say A and B ) and have fixed the cost for travelling between those pair of locations from either end  as W unit.

Now , Rohit being a curious boy wants to find the minimum cost for travelling from location U (source) to Q number of other locations (destination).

Input

First line contains N ,the number of roads that government constructed.

Next N line contains three integers A ,B, and W.

A and B represent the locations between which the road was constructed and W is the fixed cost for travelling from A to B or from B to A.

Next line contains an integer U from where Rohit wants to travel to other locations.

Next line contain Q , the number of queries (finding cost) that he wants to perform.

Next Q lines contain an integer V (destination) for which minimum cost is to be found from U.

Output

Print the required answer in each line.

If he can't travel from location U to V by any means then, print 'NO PATH' without quotes.

Example

Input:
7
0 1 4
0 3 8
1 4 1
1 2 2
4 2 3
2 5 3
3 4 2
0
4
1
4
5
7
Output:
4
5
9
NO PATH

Constraints:

1<=N<=500

0<=A,B<=500

1<=W<=100

0<=U,V<=500

1<=Q<=500

Explanation:

Query #1.

0->1: cost =4

Query #2.

0->4= 0->1->4 cost=4+1=5

Query #3.

0->5= 0->1->2->5 cost=4+2+3=9

Query #4.

0->7= no path exist between 0 and 7