After being assaulted in the parking lot by Mr. Miyagi following the \All Valley Karate Tournament", John Kreese has come to you for assistance. Help John in his quest for justice by chopping off the leaves from Mr. Miyagi's bonsai tree!

You are given an undirected tree (i.e., a connected graph with no cycles), where each edge (i.e., branch) has a nonnegative weight (i.e., thickness). One vertex of the tree has been designated the root of the tree. The remaining vertices of the tree each have unique paths to the root; non-root vertices which are not the successors of any other vertex on a path to the root are known as leaves.

Determine the minimum weight set of edges that must be removed so that none of the leaves in the original tree are connected by some path to the root.

입력

• Each test case will begin with a line containing a pair of integers n (where 1 <= n <= 1000) and r (where r ∈ {1 ,..., n }) indicating the number of vertices in the tree and the index of the root vertex, respectively.
• The next n-1 lines each contain three integers ui vi wi (where ui ,vi ∈ {1 ,..., n} and 0 <= wi <= 1000) indicating that vertex ui is connected to vertex vi by an undirected edge with weight wi.

The input will not contain duplicate edges.

출력

입출력 예

입력

15 15
1 2 1
2 3 2
2 5 3
5 6 7
4 6 5
6 7 4
5 15 6
15 10 11
10 13 5
13 14 4
12 13 3
9 10 8
8 9 2
9 11 3

출력

16

출처:standford/2009/