You are given a tree with $N$ vertices.
Here, a tree is a kind of graph, and more specifically, a connected undirected graph with $N−1$ edges, where N is the number of its vertices.
The $i$ -th edge $(1≤i≤N−1)$ connects Vertices $a_{i}$ and $b_{i}$, and has a length of $c_{i}$.

You are also given $Q$ queries and an integer $K$. In the $j$ -th query $(1≤j≤Q)$ :

find the length of the shortest path from Vertex $x_{j}$ and Vertex $y_{j}$ via Vertex $K$.

Constraints

$3≤N≤10^5$

$1≤a_{i},b_{i}≤N$  $(1≤i≤N−1)$

$1≤c_{i}≤10^9$     $(1≤i≤N−1)$

The given graph is a tree.

$1≤Q≤10^5$

$1≤K≤N$

$1≤x_{j},y_{j}≤N$  $(1≤j≤Q)$

$x_{j}≠y_{j}$  $(1≤j≤Q)$

$x_{j}≠K, y_{j}≠K$   $(1≤j≤Q)$

Input

Input is given from Standard Input in the following format:

N
a1 b1 c1 
:
aN−1 bN−1 cN−1
Q K
x1 y1
:
xQ yQ

Output

Print the responses to the queries in $Q$ lines.
In the $j$ -th line $(1≤j≤Q)$, print the response to the $j$ -th query.