PIKASONIC - Lost My Mind (feat.nakotanmaru)

You are given two points $$$(p_x,p_y)$$$ and $$$(q_x,q_y)$$$ on a Euclidean plane.

You start at the starting point $$$(p_x,p_y)$$$ and will perform $$$n$$$ operations. In the $$$i$$$-th operation, you must choose any point such that the Euclidean distance$$$^{\text{∗}}$$$ between your current position and the point is exactly $$$a_i$$$, and then move to that point.

Determine whether it is possible to reach the terminal point $$$(q_x,q_y)$$$ after performing all operations.

$$$^{\text{∗}}$$$The Euclidean distance between $$$(x_1, y_1)$$$ and $$$(x_2, y_2)$$$ is $$$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$$

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1\leq n \leq 10^3$$$) — the length of the sequence $$$a$$$.

The second line of each test case contains four integers $$$p_x,p_y,q_x,q_y$$$ ($$$1\leq p_x,p_y,q_x,q_y\leq 10^7$$$) — the coordinates of the starting point and terminal point.

The third line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le 10^4$$$) — the distance to move in each operation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, output "Yes" if it is possible to reach the terminal point $$$(q_x,q_y)$$$ after all operations; otherwise, output "No".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Note

Here is a picture that shows a possible movement of the first test case. The coordinates of point $$$r_1$$$ are $$$(3,1+\sqrt{5})$$$.

$\text{[math]}$ The first test case.

Here is a picture that shows a possible movement of the second test case. The coordinates of point $$$r_1$$$ are $$$(1+\sqrt{3},0)$$$, and the coordinates of point $$$r_2$$$ are $$$\left(-\frac{(\sqrt{3}+4)(3\sqrt{3(149-24\sqrt{3})}-7\sqrt{3}-38)}{104},-\frac{\sqrt{3(1331-764\sqrt{3})}+12\sqrt{3}-27}{104}\right)$$$.

$\text{[math]}$ The second test case.

For the third test case, it can be shown that there is no set of moves that satisfies all requirements.

Here is a picture that shows a possible movement of the fourth test case.

$\text{[math]}$ The fourth test case.

Line Segments

Examples