human
You have a permutation: an array a = [a_1, a_2, …, a_n] of distinct integers from 1 to n. The length of the permutation n is odd.

You need to sort the permutation in increasing order.

In one step, you can choose any prefix of the permutation with an odd length and reverse it. Formally, if a = [a_1, a_2, …, a_n], you can choose any odd integer p between 1 and n, inclusive, and set a to [a_p, a_{p-1}, …, a_1, a_{p+1}, a_{p+2}, …, a_n].

Find a way to sort a using no more than 5n/2 reversals of the above kind, or determine that such a way doesn't exist. The number of reversals doesn't have to be minimized.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains a single integer n (3 ≤ n ≤ 2021.
n is odd) — the length of the permutation.

The second line contains n distinct integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n) — the permutation itself. 

It is guaranteed that the sum of n over all test cases does not exceed 2021.

Output

For each test case, if it's impossible to sort the given permutation in at most 5n/2 reversals, print a single integer -1.

Otherwise, print an integer m (0 ≤ m ≤ 5n/2), denoting the number of reversals in your sequence of steps, followed by m integers p_i (1 ≤ p_i ≤ n.
p_i is odd), denoting the lengths of the prefixes of a to be reversed, in chronological order.

Note that m doesn't have to be minimized. If there are multiple answers, print any.

Example

Input

3
3
1 2 3
5
3 4 5 2 1
3
2 1 3

Output

4
3 3 3 3
2
3 5
-1

Note

In the first test case, the permutation is already sorted. Any even number of reversals of the length 3 prefix doesn't change that fact.

In the second test case, after reversing the prefix of length 3 the permutation will change to [5, 4, 3, 2, 1], and then after reversing the prefix of length 5 the permutation will change to [1, 2, 3, 4, 5].

In the third test case, it's impossible to sort the permutation.
Solve the task in PYTHON3.
 Give me a Python program to find a way to sort a using no more than 5n/2 reversals of the above kind, or determine that such a way doesn't exist?
assistant
#Here is Python program to find a way to sort a using no more than 5n/2 reversals of the above kind, or determine that such a way doesn't exist.

import sys
input = lambda: sys.stdin.readline().rstrip()

from random import shuffle
T = int(input())
for _ in range(T):
    def calcI():
        for i, a in enumerate(A):
            I[a] = i
    def addans(i):
        ANS.append(i)
        A[:i] = A[:i][::-1]
        calcI()
    
    N = int(input())
    A = [int(a) - 1 for a in input().split()]
    I = [0] * N
    k = (N - 1) // 2
    ng = 0
    for i, a in enumerate(A):
        if (i ^ a) & 1:
            ng = 1
            break
    if ng:
        print(-1)
        continue
    calcI()
    
    ANS = []
    while k:
        r = 2 * k
        l = r - 1
        if I[r] == r and I[l] == l:
            k -= 1
            continue
        if I[r] == 0 and I[l] == 1:
            addans(r + 1)
            k -= 1
            continue
        if I[r] - I[l] == 1:
            addans(I[r] + 1)
            continue
        if I[l] - I[r] == 1:
            addans(I[l] + 2)
            continue
        if I[r] == 0:
            addans(I[l])
            continue
        if I[l] > I[r]:
            addans(I[r] + 1)
            continue
        addans(I[r] + 1)
    if not ANS: ANS = [3, 3]
    print(len(ANS))
    print(*ANS)