#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using i128 = __int128;
using u128 = unsigned __int128;
template <typename T>
void chkmax(T &x, const T &y) {
  if (x < y) x = y;
}
template <typename T>
void chkmin(T &x, const T &y) {
  if (y < x) x = y;
}
constexpr int MAXN = 3e6 + 10;
int n, p[MAXN], rec[MAXN], ans[MAXN];
void solve() {
  cin >> n;
  for (int i = 1; i <= n; ++i) cin >> p[i];
  for (int r = n, l, lst = 0; r >= 1; lst = r, r = l - 1) {
    l = p[r];
    if (p[l] != l) {
      cout << "-1\n";
      return;
    }
    for (int i = l + 1, j = l; i <= r; ++i) {
      if (p[i] == l) {
        rec[i] = j;
        j = l;
      } else if (i - p[i] == j - p[j]) {
        rec[i] = j++;
      } else {
        cout << "-1\n";
        return;
      }
    }
    bool beat = !lst;
    ans[l] = (lst ? ans[r + 1] : 1);
    for (int i = l + 1, pre = l; i <= r + 1; ++i) {
      if (i == r + 1) {
        if (r + 1 + i - l <= lst && !beat) {
          ++ans[pre];
          beat = true;
          i = pre;
        }
        break;
      }
      if (p[i] == l) {
        ans[i] = ans[rec[i]] + 1;
        if (r + 1 + i - l <= lst && !beat) {
          chkmax(ans[i], ans[r + 1 + i - l]);
          beat |= (ans[i] > ans[r + 1 + i - l]);
        }
        pre = i;
      } else {
        ans[i] = ans[rec[i]];
        if (r + 1 + i - l <= lst && !beat) {
          if (ans[i] < ans[r + 1 + i - l]) {
            ++ans[pre];
            beat = true;
            i = pre;
          } else {
            beat |= (ans[i] > ans[r + 1 + i - l]);
          } 
        }
      }
    }
  }
  for (int i = 1; i <= n; ++i) cout << ans[i] << " \n"[i == n];
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int cas;
  cin >> cas;
  while (cas--) solve();
  return 0;
}
/*
g++ D.cpp -o D -std=c++14 -O2 -Wall -Wextra -Wshadow -g -fsanitize=address,undefined
*/
/*
1
3
1 2 2
*/