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A popular slogan often seen at tourist spots goes: "The wind that misses you has blown to XXX." However, rebellious travelers deliberately avoid the places where this wind supposedly blows.

Given a tourist map, please design an optimal route for rebellious travelers to get from their starting point to their destination, avoiding all locations marked with such "trendy slogans."

The "optimal route" should prioritize being the most cost-effective, meaning the total travel cost from the starting point to the destination should be minimized. If multiple routes have the same cost, the traveler prefers the one that passes through the maximum number of locations, while still avoiding all slogan-marked spots. If it is impossible to avoid these trendy locations, the traveler has no choice but to accept reality and choose the most cost-effective route that reaches the destination, while aiming to pass through the minimum number of slogan-marked locations among the equally cost-effective options.

输入格式

The first line contains two positive integers $N$ and $M$ ( $2 \le N \le 10^3$ ), representing the number of tourist locations and the number of transportation paths between them, respectively.
The next $M$ lines each contain three positive integers $A_i$ , $B_i$ , and $C_i$ ( $1 \le A_i, B_i \le N, 0 \le C_i \le 10^6, A_i \neq B_i$ ), indicating a bidirectional transportation path between locations $A_i$ and $B_i$ with a cost of $C_i$ . There are no duplicate paths between any two locations.
The following line contains a single integer $K$ ( $0 \le K \le N$ ), denoting the number of locations marked with trendy slogans.
The subsequent line lists $K$ integers separated by spaces, each representing the ID of a slogan-marked location.
The last line contains two integers $S$ and $T$ ( $1 \le S, T \le N, S \neq T$ ), indicating that the journey starts at location $S$ and ends at location $T$ . It is guaranteed that there exists at least one route from the starting point to the destination.
All location IDs are numbered starting from 1.

输出格式

Output two integers separated by a space. The first integer represents the total cost of the most cost-effective route. If the chosen route avoids all slogan-marked locations, the second integer should indicate the total number of locations passed through. Otherwise, the second integer should represent the minimum number of slogan-marked locations passed through in the route.

题目示例数据

7 10
1 2 5
1 3 3
2 4 1
3 4 2
3 5 50
3 7 20
4 6 1
4 5 0
5 7 30
5 6 10
1
4
1 6

63 5

7 10
1 2 4
1 3 3
2 4 1
3 4 2
3 5 50
3 7 20
4 6 1
4 5 0
5 7 30
5 6 10
2
4 3
1 6

6 1