<|system|>You are a helpful coding assistant.<|user|>Fix or complete the following code:

python:
Monocarp and Polycarp are learning new programming techniques. Now they decided to try pair programming.

It's known that they have worked together on the same file for n + m minutes. Every minute exactly one of them made one change to the file. Before they started, there were already k lines written in the file.

Every minute exactly one of them does one of two actions: adds a new line to the end of the file or changes one of its lines.

Monocarp worked in total for n minutes and performed the sequence of actions [a_1, a_2, ..., a_n]. If a_i = 0, then he adds a new line to the end of the file. If a_i > 0, then he changes the line with the number a_i. Monocarp performed actions strictly in this order: a_1, then a_2, ..., a_n.

Polycarp worked in total for m minutes and performed the sequence of actions [b_1, b_2, ..., b_m]. If b_j = 0, then he adds a new line to the end of the file. If b_j > 0, then he changes the line with the number b_j. Polycarp performed actions strictly in this order: b_1, then b_2, ..., b_m.

Restore their common sequence of actions of length n + m such that all actions would be correct — there should be no changes to lines that do not yet exist. Keep in mind that in the common sequence Monocarp's actions should form the subsequence [a_1, a_2, ..., a_n] and Polycarp's — subsequence [b_1, b_2, ..., b_m]. They can replace each other at the computer any number of times.

Let's look at an example. Suppose k = 3. Monocarp first changed the line with the number 2 and then added a new line (thus, n = 2, \: a = [2, 0]). Polycarp first added a new line and then changed the line with the number 5 (thus, m = 2, \: b = [0, 5]).

Since the initial length of the file was 3, in order for Polycarp to change line number 5 two new lines must be added beforehand. Examples of correct sequences of changes, in this case, would be [0, 2, 0, 5] and [2, 0, 0, 5]. Changes [0, 0, 5, 2] (wrong order of actions) and [0, 5, 2, 0] (line 5 cannot be edited yet) are not correct.
Input

The first line contains an integer t (1 ≤ t ≤ 1000). Then t test cases follow. Before each test case, there is an empty line.

Each test case contains three lines. The first line contains three integers k, n, m (0 ≤ k ≤ 100, 1 ≤ n, m ≤ 100) — the initial number of lines in file and lengths of Monocarp's and Polycarp's sequences of changes respectively.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 300).

The third line contains m integers b_1, b_2, ..., b_m (0 ≤ b_j ≤ 300).

Output

For each test case print any correct common sequence of Monocarp's and Polycarp's actions of length n + m or -1 if such sequence doesn't exist.

Example

Input

5

3 2 2
2 0
0 5

4 3 2
2 0 5
0 6

0 2 2
1 0
2 3

5 4 4
6 0 8 0
0 7 0 9

5 4 1
8 7 8 0
0

Output

2 0 0 5
0 2 0 6 5
-1
0 6 0 7 0 8 0 9
-1<|assistant|>Here's the solution:


<|system|>You are a helpful coding assistant.<|user|>Fix or complete the following code:

python:
4 different points on the plane Read the coordinates of $ A (x_a, y_a) $, $ B (x_b, y_b) $, $ C (x_c, y_c) $, $ D (x_d, y_d) $ and read those 4 points Create a program that outputs YES if there is no dent in the quadrangle $ ABCD $ with the coordinates as the vertices, and NO if there is a dent.

A quadrangle with a dent is a quadrangle as shown in Figure 1.

<image>
Input

Given multiple datasets. The format of each dataset is as follows.

$ x_a $, $ y_a $, $ x_b $, $ y_b $, $ x_c $, $ y_c $, $ x_d $, $ y_d $

$ x_a $, $ y_a $, $ x_b $, $ y_b $, $ x_c $, $ y_c $, $ x_d $, $ y_d $ are -100 or more and 100 or less, respectively, and are given as real numbers.

1 No more than two points can be lined up on a straight line. Also, if you connect the points in the order of input, the coordinates of the points will be input in the order of forming a quadrangle. (That is, the points are not given in the order shown in Figure 2.)

The number of datasets does not exceed 100.

Output

Print YES or NO on one line for each dataset.

Example

Input

0.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0
0.0,0.0,3.0,0.0,1.0,1.0,1.0,3.0

Output

YES
NO<|assistant|>Here's the solution:


<|system|>You are a helpful coding assistant.<|user|>Fix or complete the following code:

python:
You are given an equation:

Ax2 + Bx + C = 0.

Your task is to find the number of distinct roots of the equation and print all of them in ascending order.
Input

The first line contains three integer numbers A, B and C ( - 105 ≤ A, B, C ≤ 105). Any coefficient may be equal to 0.

Output

In case of infinite root count print the only integer -1. In case of no roots print the only integer 0. In other cases print the number of root on the first line and the roots on the following lines in the ascending order. Print roots with at least 5 digits after the decimal point.

Examples

Input

1 -5 6

Output

2
2.0000000000
3.0000000000<|assistant|>Here's the solution:


<|system|>You are a helpful coding assistant.<|user|>Fix or complete the following code:

python:
Given a string s. Can you make it a palindrome by deleting exactly one character? Note that size of the string after deletion would be one less than it was before.
Input
First line of the input contains a single integer T denoting number of test cases.
For each test case, you are given a single line containing string  s.

Output
For each test case, print YES or NO depending on the answer of the problem.

Constraints

 Example
Input:
4
aaa
abc
abdbca
abba

Output:
YES
NO
YES
YES

Explanation
Example case 1. Delete any one 'a', resulting string is "aa" which is a palindrome.
Example case 2. It is not possible to delete exactly one character and having a palindrome.
Example case 3. Delete 'c', resulting string is "abdba" which is a palindrome.
Example case 4. Delete 'b', resulting string is "aba" which is a palindrome.<|assistant|>Here's the solution: