#include<bits/stdc++.h>
#pragma GCC optimize(2)
using namespace std;
int t, n, to[500005], col[500005], a[500005], b[500005], pre[500005], flg, fflg, cnt, vis[500005], aans;
inline void recheck() {
	for (int i = 1; i <= cnt; i++) vis[i] = 0;
	aans = 0;
	int rr = 0;
	//	cout << cnt << ' ' << aans << ' ' << flg << "@\n";
	for (int i = 1; i <= n; i++) {
		if (!col[i]) flg = 0;
		while (aans < cnt && rr != n) {
			rr++;
			vis[col[rr]]++;
			if (vis[col[rr]] == 1) aans++;
		}
		//		cout << rr << ' ' << aans << ' ' << i << "**\n";
		if (a[i] == n + 1) {
			if (aans == cnt) flg = 0;
		} else if (a[i] != rr || aans != cnt) {
			flg = 0;
		}
		vis[col[i]]--;
		if (!vis[col[i]]) aans--;
	}
}
inline bool check(int p) {
	int now = p - 1;
	for (int i = 1; i <= n; i++) {
		if (!pre[i] && !col[i] && !now) return false;
		if (to[i]) now--;
		if (pre[i]) now++;
	}
	return true;
}
inline int gets() {
	int l = 1, r = a[1] + 1;
	int mid = (l + r) >> 1;
	while (l < r) {
		mid = (l + r) >> 1;
		if (check(mid)) r = mid;
		else l = mid + 1;
	}
	return l;
}
signed main() {
	//freopen("sing.in", "r", stdin);
	//freopen("sing.out", "w", stdout);
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin >> t;
	while (t--) {
		cin >> n;
		for (int i = 1; i <= n; i++) col[i] = pre[i] = to[i] = 0;
		flg = 0, fflg = 1;
		for (int i = 1; i <= n; i++) {
			cin >> a[i];
			if (a[i] == i) flg = 1;
			else fflg = 0;
			if (i ^ 1 && a[i] != a[i - 1]) {
				pre[a[i]] = i - 1;
				to[i - 1] = a[i];
			}
		}
		if (flg || a[1] == n + 1 || pre[a[1]]) {
			if (!fflg || a[1] == n + 1 || pre[a[1]]) {
				cout << "-1\n";
			} else {
			//	cout << "YES\n";
				for (int i = 1; i <= n; i++) cout << 1 << " ";
				cout << "\n";
			}
			continue;
		}
		//		for (int i = 1; i <= n; i++) cout << pre[i] << " " << to[i] << "&&\n";
		pre[a[1]] = a[1];
		int op = gets();
		//		cout << op << '*';

		if (op > a[1]) {
			cout << "-1\n";
			continue;
		}
		pre[a[1]] = 0;
		flg = 1;
		int rr = 0;
		set<pair<int, int>> s;
		col[a[1]] = op;
		for (int i = 1; i < op; i++) s.insert(make_pair(0, i)) ;
		s.insert(make_pair(a[1], op));
		cnt = 0;
		cnt = op;
		for (int i = 1; i <= n; i++) {
			if (pre[i]) {
				col[i] = col[pre[i]];
				s.insert(make_pair(i, col[i]));
			}
			if (!col[i]) {
				pair<int, int> ops = (*s.begin());
				s.erase(s.begin());
				col[i] = ops.second;
				s.insert(make_pair(i, col[i]));
			}

			if (to[i]) {
				s.erase(make_pair(i, col[i]));
			}

		}
		//		for (int i = 1; i <= n; i++) {
		//			cout << col[i] << " " << i << " " << pre[i] << " " << to[i] << ' ' << a[i] << "!\n";
		//		}
		//		cout << flg << "||\n";
		recheck();
		if (!flg) {
			cout << "-1\n";
		} else {
	//		cout << "YES\n";
			for (int i = 1; i <= n; i++) cout << col[i] << ' ';
			cout << "\n";
		}
	}
}