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.
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 random

tc = int(input())
while tc > 0:
    tc -= 1
    # n = 5
    n = int(input())

    def gen():
        even = list(range(0, n, 2))
        odd = list(range(1, n, 2))
        random.shuffle(even)
        random.shuffle(odd)
        return [odd[i // 2] if i % 2 else even[i // 2] for i in range(n)]

    a = list(map(lambda x: int(x) - 1, input().split()))
    # a = gen()
    if any((i + a[i]) % 2 for i in range(n)):
        print(-1)
    else:
        ans = []

        def rev(i):
            global a, ans
            assert i % 2 == 1 and i <= n
            a[:i] = a[i - 1::-1]
            ans += [i]

        for i in range(n - 2, -1, -2):
            while True:
                if a[i] == i and a[i + 1] == i + 1:
                    break
                if a[0] == i + 1 and a[1] == i:
                    rev(i + 2)
                elif abs(a.index(i) - a.index(i + 1)) == 1:
                    rev(a.index(i) + 2)
                elif a[0] == i + 1:
                    rev(a.index(i))
                else:
                    rev(a.index(i + 1) + 1)
            assert all(j == a[j] for j in range(i, n))
        print(len(ans))
        print(*ans)