#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <class T>
using vv = vector<vector<T>>;
template <class T>
inline bool MX(T &l, const T &r) {
  return l < r ? l = r, 1 : 0;
}
template <class T>
inline bool MN(T &l, const T &r) {
  return l > r ? l = r, 1 : 0;
}
void ouT(ll x, int d = 3) {
  auto re = to_string(x);
  if ((int)re.size() > d) re = x > 0 ? "oo" : "-oo";
  cout << string(d - re.size(), ' ') << re << ",";
}
template <class A, class B>
pair<A, B> operator+(const pair<A, B> &p, const pair<A, B> &q) {
  return {p.first + q.first, p.second + q.second};
}
template <class A, class B, class C, class D>
pair<A, B> &operator+=(pair<A, B> &p, const pair<C, D> &q) {
  p.first += q.first;
  p.second += q.second;
  return p;
}
template <class A, class B>
pair<A, B> operator-(const pair<A, B> &p, const pair<A, B> &q) {
  return {p.first - q.first, p.second - q.second};
}
template <class A, class B, class C, class D>
pair<A, B> &operator-=(pair<A, B> &p, const pair<C, D> &q) {
  p.first -= q.first;
  p.second -= q.second;
  return p;
}
template <class A, class B>
istream &operator>>(istream &is, pair<A, B> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T = ll>
T read() {
  T re;
  cin >> re;
  return re;
}
template <class T = ll>
T read(const T &dec) {
  T re;
  cin >> re;
  return re - dec;
}
template <class T = ll>
vector<T> readV(const int sz) {
  vector<T> re(sz);
  for (auto &x : re) x = read<T>();
  return re;
}
template <class T = ll>
vector<T> readV(const int sz, const T &dec) {
  vector<T> re(sz);
  for (auto &x : re) x = read<T>(dec);
  return re;
}
vv<int> readG(const int &n, const int &m) {
  vv<int> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    g[a].push_back(b);
    g[b].push_back(a);
  }
  return g;
}
vv<int> readG(const int &n) { return readG(n, n - 1); }
vv<int> readD(const int &n, const int &m) {
  vv<int> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    g[a].push_back(b);
  }
  return g;
}
vv<int> readD(const int &n) { return readD(n, n - 1); }
template <class T>
vv<pair<int, T>> readG(const int &n, const int &m) {
  vv<pair<int, T>> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    const auto c = read<T>();
    g[a].emplace_back(b, c);
    g[b].emplace_back(a, c);
  }
  return g;
}
template <class T>
vv<pair<int, T>> readG(const int &n) {
  return readG<T>(n, n - 1);
}
template <class T>
vv<pair<int, T>> readD(const int &n, const int &m) {
  vv<pair<int, T>> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    const auto c = read<T>();
    g[a].emplace_back(b, c);
  }
  return g;
}
template <class T>
vv<pair<int, T>> readD(const int &n) {
  return readD<T>(n, n - 1);
}
const ll MOD = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(0);
  const auto TTT = read();
  for (int(_) = 0; (_) < (int)(TTT); ++(_)) {
    const auto n = read();
    auto vs = readV(n, 1);
    {
      int ok = 1;
      for (int(i) = 0; (i) < (int)(n); ++(i))
        if ((i + vs[i]) % 2) ok = 0;
      if (!ok) {
        cout << -1 << "\n";
        continue;
      }
    }
    vector<int> re;
    const auto rev = [&](const int &len) {
      re.emplace_back(len);
      reverse(vs.begin(), vs.begin() + len);
      ;
    };
    for (int(v) = (int)(n)-1; (v) >= 0; --(v))
      if (v % 2) {
        const auto a = v;
        const auto b = v + 1;
        ;
        auto ai = find((vs).begin(), (vs).end(), a) - vs.begin();
        auto bi = find((vs).begin(), (vs).end(), b) - vs.begin();
        if (abs(ai - bi) > 1) {
          rev(bi + 1);
          ai = find((vs).begin(), (vs).end(), a) - vs.begin();
          rev(ai);
          bi = ai - 1;
        }
        if (bi + 1 == ai) {
          rev(ai + 2);
          ai = 1;
          bi = 2;
        }
        if (ai != a) {
          rev(bi + 1);
          rev(b + 1);
        };
      }
    int ok = 1;
    for (int(i) = 0; (i) < (int)(n); ++(i))
      if (i != vs[i]) ok = 0;
    if (ok) {
      cout << re.size() << "\n";
      for (const auto &x : re) cout << x << " ";
      cout << "\n";
    } else {
      cout << -1 << "\n";
    }
  }
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <class T>
using vv = vector<vector<T>>;
template <class T>
inline bool MX(T &l, const T &r) {
  return l < r ? l = r, 1 : 0;
}
template <class T>
inline bool MN(T &l, const T &r) {
  return l > r ? l = r, 1 : 0;
}
void ouT(ll x, int d = 3) {
  auto re = to_string(x);
  if ((int)re.size() > d) re = x > 0 ? "oo" : "-oo";
  cout << string(d - re.size(), ' ') << re << ",";
}
template <class A, class B>
pair<A, B> operator+(const pair<A, B> &p, const pair<A, B> &q) {
  return {p.first + q.first, p.second + q.second};
}
template <class A, class B, class C, class D>
pair<A, B> &operator+=(pair<A, B> &p, const pair<C, D> &q) {
  p.first += q.first;
  p.second += q.second;
  return p;
}
template <class A, class B>
pair<A, B> operator-(const pair<A, B> &p, const pair<A, B> &q) {
  return {p.first - q.first, p.second - q.second};
}
template <class A, class B, class C, class D>
pair<A, B> &operator-=(pair<A, B> &p, const pair<C, D> &q) {
  p.first -= q.first;
  p.second -= q.second;
  return p;
}
template <class A, class B>
istream &operator>>(istream &is, pair<A, B> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T = ll>
T read() {
  T re;
  cin >> re;
  return re;
}
template <class T = ll>
T read(const T &dec) {
  T re;
  cin >> re;
  return re - dec;
}
template <class T = ll>
vector<T> readV(const int sz) {
  vector<T> re(sz);
  for (auto &x : re) x = read<T>();
  return re;
}
template <class T = ll>
vector<T> readV(const int sz, const T &dec) {
  vector<T> re(sz);
  for (auto &x : re) x = read<T>(dec);
  return re;
}
vv<int> readG(const int &n, const int &m) {
  vv<int> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    g[a].push_back(b);
    g[b].push_back(a);
  }
  return g;
}
vv<int> readG(const int &n) { return readG(n, n - 1); }
vv<int> readD(const int &n, const int &m) {
  vv<int> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    g[a].push_back(b);
  }
  return g;
}
vv<int> readD(const int &n) { return readD(n, n - 1); }
template <class T>
vv<pair<int, T>> readG(const int &n, const int &m) {
  vv<pair<int, T>> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    const auto c = read<T>();
    g[a].emplace_back(b, c);
    g[b].emplace_back(a, c);
  }
  return g;
}
template <class T>
vv<pair<int, T>> readG(const int &n) {
  return readG<T>(n, n - 1);
}
template <class T>
vv<pair<int, T>> readD(const int &n, const int &m) {
  vv<pair<int, T>> g(n);
  for (int(_) = 0; (_) < (int)(m); ++(_)) {
    const auto a = read<int>(1), b = read<int>(1);
    const auto c = read<T>();
    g[a].emplace_back(b, c);
  }
  return g;
}
template <class T>
vv<pair<int, T>> readD(const int &n) {
  return readD<T>(n, n - 1);
}
const ll MOD = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(0);
  const auto TTT = read();
  for (int(_) = 0; (_) < (int)(TTT); ++(_)) {
    const auto n = read();
    auto vs = readV(n, 1);
    {
      int ok = 1;
      for (int(i) = 0; (i) < (int)(n); ++(i))
        if ((i + vs[i]) % 2) ok = 0;
      if (!ok) {
        cout << -1 << "\n";
        continue;
      }
    }
    vector<int> re;
    const auto rev = [&](const int &len) {
      re.emplace_back(len);
      reverse(vs.begin(), vs.begin() + len);
      ;
    };
    for (int(v) = (int)(n)-1; (v) >= 0; --(v))
      if (v % 2) {
        const auto a = v;
        const auto b = v + 1;
        ;
        auto ai = find((vs).begin(), (vs).end(), a) - vs.begin();
        auto bi = find((vs).begin(), (vs).end(), b) - vs.begin();
        if (abs(ai - bi) > 1) {
          rev(bi + 1);
          ai = find((vs).begin(), (vs).end(), a) - vs.begin();
          rev(ai);
          bi = ai - 1;
        }
        if (bi + 1 == ai) {
          rev(ai + 2);
          ai = 1;
          bi = 2;
        }
        if (ai != a) {
          rev(bi + 1);
          rev(b + 1);
        };
      }
    int ok = 1;
    for (int(i) = 0; (i) < (int)(n); ++(i))
      if (i != vs[i]) ok = 0;
    if (ok) {
      cout << re.size() << "\n";
      for (const auto &x : re) cout << x << " ";
      cout << "\n";
    } else {
      cout << -1 << "\n";
    }
  }
  return 0;
}

```