Problem B

Minimum Transport Cost

Input file: trans.in

These are N cities in Spring country. Between each pair of cities there may be one transportation track or none. Now there is some cargo that should be delivered from one city to another. The transportation fee consists of two parts:

The cost of the transportation on the path between these cities, and
a certain tax which will be charged whenever any cargo passing through one city, except for the source and the destination cities.

You must write a program to find the route which has the minimum cost.

Input

The data of path cost, city tax, source and destination cities are given in the file trans.in, which is of the form:

..................

where is the transport cost from city i to city j, =-1 indicates there is no direct path between city i and city j. represents the tax of passing through city i. And the cargo is to be delivered from city c to city d, city e to city f, ........, and city g to city h. You must output the sequence of cities passed by and the total cost which is of the form:

Output

From c to d:
path: c-->c1-->......-->ck-->d
Total cost: ......
......

From e to f:
path: e-->e1-->..........-->ek-->f
Total cost: ......

Sample Input

0 3 22 -1 4
3 0 5 -1 -1
22 5 0 9 20
-1 -1 9 0 4
4 -1 20 4 0
5 17 8 3 1
1 3
3 5
2 4

Output for the Sample Input

From 1 to 3 :
Path: 1-->5-->4-->3
Total cost : 21

From 3 to 5 :
Path: 3-->4-->5
Total cost : 16

From 2 to 4 :
Path: 2-->1-->5-->4
Total cost : 17