ChonSu

The genealogy of a family can be represented as a rooted tree, in which each node corresponds to a member of the family and each edge connects a member to their parent. The root is the founder of the family and has no parent in the genealogy; leaf nodes correspond to members with no children.

The distance between two members in a genealogy is called a ChonSu in Korea, and it is defined as the number of edges on the path between them. For example, in the genealogy shown below, the ChonSu between persons 1 and 3 is 3, while the ChonSu between persons 1 and 5 is 5. From now on, the ChonSu between person $i$ and person $j$ is written ChonSu(i, j).

A rooted tree in which every node that is not a leaf has exactly two children is called a 2-tree. In other words, a 2-tree is a binary tree in which each node has either two children or none. The tree shown above is a 2-tree.

Consider a family whose complete genealogy is unknown. What is known is that the genealogy is a 2-tree with $n$ leaf nodes. Assume the leaf nodes are numbered $1, 2, \ldots, n$ from left to right as in the figure. Also known is the ChonSu between every pair of leaf nodes whose numbers are consecutive; that is, ChonSu(i, i+1) is known for every $i$ ($1 \le i \le n-1$).

It is well known that this information alone is enough to compute the ChonSu between any two leaf nodes.

Write a program that, given two leaf members $x$ and $y$ ($1 \le x < y \le n$), computes ChonSu(x, y).

For the figure above you are given $n = 6$, ChonSu(1, 2) = 3, ChonSu(2, 3) = 2, ChonSu(3, 4) = 5, ChonSu(4, 5) = 3, and ChonSu(5, 6) = 2, and from this you can compute ChonSu(1, 6), the ChonSu between $x = 1$ and $y = 6$.

The input consists of several test cases. The first line contains the number of test cases $T$. For each test case, the first line contains an integer $n$ ($3 \le n \le 1000$), the number of leaf nodes. The next line contains $n-1$ integers ChonSu(1, 2), ChonSu(2, 3), ..., ChonSu(n-1, n) in order. The last line contains two integers $x$ and $y$ ($1 \le x < y \le n$), the numbers of the two leaf members whose ChonSu is to be computed.

For each test case, print exactly one line containing a single integer: the ChonSu between the two leaf nodes $x$ and $y$.