You are given a table a of size 2 × n (i.e. two rows and n columns) consisting of integers from 1 to n.

In one move, you can choose some column j (1 ≤ j ≤ n) and swap values a_{1, j} and a_{2, j} in it. Each column can be chosen no more than once.

Your task is to find the minimum number of moves required to obtain permutations of size n in both first and second rows of the table or determine if it is impossible to do that.

You have to answer t independent test cases.

Recall that the permutation of size n is such an array of size n that contains each integer from 1 to n exactly once (the order of elements doesn't matter).

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of columns in the table. The second line of the test case contains n integers a_{1, 1}, a_{1, 2}, ..., a_{1, n} (1 ≤ a_{1, i} ≤ n), where a_{1, i} is the i-th element of the first row of the table. The third line of the test case contains n integers a_{2, 1}, a_{2, 2}, ..., a_{2, n} (1 ≤ a_{2, i} ≤ n), where a_{2, i} is the i-th element of the second row of the table.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case print the answer: -1 if it is impossible to obtain permutation of size n in both first and the second rows of the table, or one integer k in the first line, where k is the minimum number of moves required to obtain permutations in both rows, and k distinct integers pos_1, pos_2, ..., pos_k in the second line (1 ≤ pos_i ≤ n) in any order — indices of columns in which you need to swap values to obtain permutations in both rows. If there are several answers, you can print any.

Example

Input


6
4
1 2 3 4
2 3 1 4
5
5 3 5 1 4
1 2 3 2 4
3
1 2 1
3 3 2
4
1 2 2 1
3 4 3 4
4
4 3 1 4
3 2 2 1
3
1 1 2
3 2 2


Output


0

2
2 3 
1
1 
2
3 4 
2
3 4 
-1
#include <bits/stdc++.h>
using namespace std;
template <class T>
void debug(vector<T>& v) {
  for (int i = 0; i < (v.size()); i++) {
    cout << v[i] << (i == v.size() - 1 ? '\n' : ' ');
  }
}
int main() {
  int t;
  cin >> t;
  for (int i = 0; i < (t); i++) {
    int n;
    cin >> n;
    vector<int> a1(n);
    vector<int> a2(n);
    vector<vector<int> > b(n);
    vector<int> visited(n, 0);
    for (int j = 0; j < (n); j++) {
      cin >> a1[j];
      a1[j]--;
      b[a1[j]].push_back(j);
    }
    for (int j = 0; j < (n); j++) {
      cin >> a2[j];
      a2[j]--;
      b[a2[j]].push_back(j);
    }
    bool bad = false;
    for (int i = 0; i < n; ++i) {
      if (b[i].size() != 2) {
        bad = true;
      }
    }
    if (bad) {
      cout << -1 << endl;
      continue;
    }
    int count = 0;
    vector<int> change;
    for (int j = 0; j < (n); j++) {
      if (visited[j]) {
        continue;
      }
      vector<int> cols;
      vector<int> change_cols;
      cols.push_back(j);
      visited[j] = true;
      while (a1[j] != a2[cols.back()]) {
        int other_index = cols.back() == b[a2[cols.back()]][0]
                              ? b[a2[cols.back()]][1]
                              : b[a2[cols.back()]][0];
        if (a2[cols.back()] == a1[other_index]) {
          cols.push_back(other_index);
        } else {
          swap(a1[other_index], a2[other_index]);
          change_cols.push_back(other_index);
          cols.push_back(other_index);
        }
        visited[other_index] = true;
      }
      if (change_cols.size() < cols.size() - change_cols.size()) {
        count += change_cols.size();
        for (auto x : change_cols) {
          change.push_back(x + 1);
        }
      } else {
        count += cols.size() - change_cols.size();
        set<int> set_change_cols(change_cols.begin(), change_cols.end());
        for (auto x : cols) {
          if (set_change_cols.find(x) == set_change_cols.end()) {
            change.push_back(x + 1);
          }
        }
      }
    }
    cout << count << endl;
    if (count == 0) {
      cout << endl;
    } else {
      for (int i = 0; i < change.size(); ++i) {
        cout << change[i] << (i == change.size() - 1 ? "\n" : " ");
      }
    }
  }
}
