The word of sponsor#34
At the end of the "New Year Night" tournament, the sponsor decided to send prizes by post. Knowing the number of participants and the delivery times between some departments of "Ukrpost", determine after how long the last prize-winner will receive their prize.
The first line contains three integers: the number of participants , the number of prizes , and the number of known delivery times between some departments.
The next line contains the numbers of postal departments of the participants who became prize-winners, separated by spaces.
Then follow lines, each containing three numbers describing the delivery time between two post departments in the format: , where and are the department numbers, and (0 \le t \le 365) is the delivery time between them.
The last line contains one number—the number of the post department from which the sponsor will send the prizes. It is guaranteed that 1 \le n,\, m,\, a,\, b \le 365. Each participant corresponds to their own department.
If all prizes are delivered to the winners, print on the first line The good sponsor! and on the second line the time at which the last prize-winner receives their prize.
If at least one winner cannot receive their prize, output a single line It is not fault of sponsor.... Print the phrases without quotation marks.
Example 1