Problem Statement

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
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}
Q K
x_1 y_1
:
x_{Q} y_{Q}

Output

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