#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <array>
#include <iomanip>
#include <utility>
#include <tuple>
#include <functional>
#include <bitset>
#include <cassert>
#include <complex>
#include <stdio.h>
#include <time.h>
#include <numeric>
#include <random>
#include <unordered_set>
#include <unordered_map>
#define all(a) (a).begin(), (a).end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define req(i, a, b) for (ll i = (a); i < (b); i++)
#define pb push_back
#define debug(x) cerr << __LINE__ << ' ' << #x << ':' << (x) << '\n'
#define debug2(x, y) cerr << __LINE__ << ' ' << #x << ':' << (x) << ',' << #y << ':' << (y) << '\n'
#define debug3(x, y, z) cerr << __LINE__ << ' ' << #x << ':' << (x) << ',' << #y << ':' << (y) << ',' << #z << ':' << (z) << '\n'
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef long double ld;
template<class T> using P = pair<T, T>;
template<class T> using pri_l = priority_queue<T>;
template<class T> using pri_s = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = 1000000010;
constexpr int inf2 = 2000000010;
constexpr ll INF = 1000000000000000010;
constexpr ll INF4 = 4000000000000000010;
constexpr int mod1e9 = 1000000007;
constexpr int mod998 = 998244353;
constexpr ld eps = 1e-12;
constexpr ld pi = 3.141592653589793238;
constexpr ll ten(int n) { return n ? 10 * ten(n - 1) : 1; };
int dx[] = { 1,0,-1,0,1,1,-1,-1,0 }; int dy[] = { 0,1,0,-1,1,-1,1,-1,0 };
ll mul(ll a, ll b) { return (b != 0 && a > INF / b ? INF : a * b); }
void fail() { cout << "-1\n"; exit(0); } void no() { cout << "No\n"; exit(0); }
template<class T> void er(T a) { cout << a << '\n'; exit(0); }
template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return true; } return false; }
template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return true; } return false; }
template<class T> istream& operator >>(istream& s, vector<T>& v) { for (auto& e : v) s >> e; return s; }
template<class T> ostream& operator <<(ostream& s, const vector<T>& v) { for (auto& e : v) s << e << ' '; return s; }
template<class T, class U> ostream& operator << (ostream& s, const pair<T, U>& p) { s << p.first << ' ' << p.second; return s; }

struct fastio {
	fastio() {
		cin.tie(0); cout.tie(0);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(20);
		cerr << fixed << setprecision(20);
	}
}fastio_;

namespace rdv {
	random_device seed_gen;
	mt19937_64 engine(seed_gen());
	ll rnum(ll r) { return engine() % r; } // [0, r)
	ll rnum(ll l, ll r) { return rnum(r - l) + l; } // [l, r)
	ll rng(ll l, ll r) { return rnum(l, r + 1); } // [l, r]
	double rng01() { return engine() * pow(2, -64); }
	template<class T> void shuf(vector<T>& v) { shuffle(all(v), engine); }
	void shuf(string& s) { shuffle(all(s), engine); }
}

using namespace rdv;

template<class T> vector<int> compress(vector<T> v) {
	int n = v.size();
	vector<T> tmp = v;
	sort(tmp.begin(), tmp.end());
	tmp.erase(unique(tmp.begin(), tmp.end()), tmp.end());
	vector<int> res(n);
	for (int i = 0; i < n; i++) res[i] = lower_bound(tmp.begin(), tmp.end(), v[i]) - tmp.begin();
	return res;
}

#include <atcoder/all>
using namespace atcoder;

constexpr ll mod = mod998;
using mint = static_modint<mod>;

istream& operator >>(istream& s, mint& m) { ll y; s >> y; m = y; return s; }
ostream& operator <<(ostream& s, mint& m) { return s << m.val(); }
ostream& operator <<(ostream& s, const vector<mint>& v) { for (auto& e : v) s << e.val() << ' '; return s; }

vector<mint> fac, inv, facinv;

void modcalc(int n) {
	fac.resize(n); inv.resize(n); facinv.resize(n);
	fac[0] = 1; fac[1] = 1; inv[1] = 1;
	facinv[0] = 1; facinv[1] = 1;
	for (ll i = 2; i < n; i++) {
		fac[i] = fac[i - 1] * i;
		inv[i] = -inv[mod % i] * (mod / i);
		facinv[i] = facinv[i - 1] * inv[i];
	}
}

mint comb(ll n, ll k) {
	if (n < 0 || k < 0 || n < k) return 0;
	return fac[n] * facinv[k] * facinv[n - k];
}

mint perm(ll n, ll k) {
	if (n < 0 || k < 0 || n < k) return 0;
	return fac[n] * facinv[n - k];
}

mint hom(ll n, ll k) {
	if (n < 0 || k < 0 || n == 0 && k > 0) return 0;
	if (n == 0 && k == 0) return 1;
	return fac[n + k - 1] * facinv[k] * facinv[n - 1];
}

int main() {

	bool DEBUG = false;

	// 手数減らないのか～
	/*vector<vector<int>> S = { {3,1,0,2},{1,3,2,0},{0,2,3,1},{2,0,1,3} };
	map<vector<int>, vector<int>> mp;
	mp[{0, 1, 2, 3}] = {};
	rep(i, 4) mp[S[i]] = { int(i) };
	rep(i, 4) {
		rep(j, 4) {
			vector<int> p(4);
			rep(k, 4) p[k] = k;
			rep(k, 4) p[k] = S[i][p[k]];
			rep(k, 4) p[k] = S[j][p[k]];
			debug(p);
			mp[p] = { int(i),int(j) };
		}
	}

	for (auto [key, val] : mp) {
		debug2(key, val);
	}*/

	int TEST = 1;
	cin >> TEST;
	while (TEST--) {
		int n;
		cin >> n;

		auto f = [&](int i, int j) -> int {
			return i * n + j + 1;
		};

		vector a(n, vector<int>(n));
		rep(i, n) rep(j, n) {
			if (0 && DEBUG) a[i][j] = i * n + j + 1;
			else cin >> a[i][j];
		}

		bool bad = false;
		rep(i, n) rep(j, n) {
			if (a[i][j] != f(i, j) && a[i][j] != f(i, n - 1 - j) && a[i][j] != f(n - 1 - i, j) && a[i][j] != f(n - 1 - i, n - 1 - j)) bad = true;
		}

		if (bad) {
			cout << "-1\n";
			continue;
		}

		int last = 2;
		vector<int> ans;
		auto op = [&](int type, int v) -> void {
			assert(type != last);
			last = type;
			ans.push_back(v + 1);
			if (1) {
				if (type == 1) reverse(all(a[v]));
				else {
					rep(i, n / 2) swap(a[i][v], a[n - 1 - i][v]);
				}
			}
		};

		// A_i + B_j のパリティが決まっている

		int t = (n + 1) / 2;
		vector G(t, vector<int>(t));

		rep(i, t) {
			rep(j, t) {
				int x = n - 1 - i, y = n - 1 - j;
				vector<int> vec;
				vec.push_back(a[i][j]);
				if (j != y) vec.push_back(a[i][y]);
				if (i != x) vec.push_back(a[x][j]);
				if (i != x && j != y) vec.push_back(a[x][y]);
				int p = 0;
				int s = ssize(vec);
				rep(k, s) rep(l, k) if (vec[k] < vec[l]) p ^= 1;
				G[i][j] = p;
			}
		}

		vector<int> A(t), B(t);
		rep(i, t) B[i] = G[0][i];

		if (n % 2 == 1) B[t - 1] = G[0][t - 1];
		for (int i = 1; i < t; i++) A[i] = B[0] ^ G[i][0];
		if (n % 2 == 1) A[t - 1] = G[t - 1][0];

		rep(i, t) rep(j, t) {
			if (n % 2 == 1 && i == t - 1 && j == t - 1) {
				// なんでも OK
			}
			else if (n % 2 == 1 && i == t - 1) {
				if (A[i] != G[i][j]) bad = true;
			}
			else if (n % 2 == 1 && j == t - 1) {
				if (B[j] != G[i][j]) bad = true;
			}
			else {
				if ((A[i] ^ B[j]) != G[i][j]) bad = true;
			}
		}

		if (bad) {
			cout << "-1\n";
			continue;
		}

		// debug2(A, B);

		bool rev = false;
		vector<int> av, bv;
		rep(i, t) {
			if (A[i]) av.push_back(i);
			if (B[i]) bv.push_back(i);
		}

		while (true) {
			int as = ssize(av), bs = ssize(bv);
			if (as == bs) break;
			if (as == bs + 1) {
				rev = true;
				break;
			}
			if (as > bs) rep(_, 2) bv.push_back(0);
			if (as < bs) rep(_, 2) av.push_back(0);
		}

		// debug2(av, bv);

		rep(i, ssize(av)) {
			op(1, av[i]);
			if (i < ssize(bv)) op(2, bv[i]);
		}

		// rep(i, n) rep(j, n) cerr << a[i][j] << " \n"[j == n - 1];

		rep(i, t) {
			rep(j, t) {
				// 12 手以内
				int x = n - 1 - i, y = n - 1 - j;
				if (i == x or j == y) continue;
				if (a[i][j] == f(x, y)) {
					if (!rev) { op(1, x); op(2, j); op(1, x); op(2, j); }
					else { op(2, y); op(1, i); op(2, y); op(1, i); }
				}
				else if (a[i][y] == f(x, y)) {
					if (!rev) { op(1, i); op(2, y); op(1, i); op(2, y); }
					else { op(2, y); op(1, x); op(2, y); op(1, x); }
				}
				else if (a[x][j] == f(x, y)) {
					if (!rev) { op(1, x); op(2, y); op(1, x); op(2, y); }
					else { op(2, j); op(1, x); op(2, j); op(1, x); }
				}
				while (a[x][j] != f(x, j)) {
					if (!rev) { op(1, i); op(2, j); op(1, i); op(2, j); }
					else { op(2, j); op(1, i); op(2, j); op(1, i); }
				}
				if (a[i][j] != f(i, j)) bad = true;
			}
		}

		// rep(i, n) rep(j, n) cerr << a[i][j] << " \n"[j == n - 1];
		rep(i, n) rep(j, n) assert(a[i][j] == f(i, j));

		// 3N^2 + O(N) 回

		int sz = ssize(ans);
		cout << sz << '\n';
		assert(sz <= 4 * n * n);
		rep(i, sz) cout << ans[i] << " \n"[i == sz - 1];
	}

}