/**
 *    author: sunkuangzheng
 *    created: 26.06.2024 20:43:34
**/
#include<bits/stdc++.h>
#ifdef DEBUG_LOCAL
#include <mydebug/debug.h>
#endif
using ll = long long;
const int N = 5e5+5;
using namespace std;
int T,n,s[N],a[N],al[N],ar[N],pre[N],vl[N];
void los(){
    cin >> n;
    for(int i = 1;i <= n;i ++) cin >> a[i];
    int pos = n; 
    while(pos >= 1){
        for(int i = a[pos];i <= pos;i ++) al[i] = a[pos],ar[i] = pos;
        pos = a[pos] - 1;
    }for(int i = 1;i <= n;i ++) if(a[i] < al[i]) return cout << "-1\n",void();
    int i = 2,j = 1;
    for(;i <= n;){
        if(a[i] == al[i]) pre[i] = j,vl[i] = 1,j = a[i ++];
        else if(j - a[j] == i - a[i]) pre[i] = j ++,vl[i ++] = 0;
        else return cout << "-1\n",void();
    }pre[1] = 1,vl[1] = 1;
    for(int j = al[n];j >= 1;j = al[j - 1]){
        int fg = 0; 
        for(int i = j;i <= ar[j];i ++){
            s[i] = s[pre[i]] + vl[i]; int val = s[ar[j] + 1 + i - al[j]],nxtl = ar[j] + 1 + i - al[j];
            if(ar[j] != n && (s[i] < val && !fg || s[i] <= val && nxtl != ar[nxtl] && i == ar[j] && !fg)){
                fg = 1; 
                while(!vl[i]) i --;
                s[i] ++;
            }else if(ar[j] != n && s[i] > val) fg = 1;
        }
    }for(int i = 1;i <= n;i ++) cout << s[i] << " ",s[i] = 0;
    cout << "\n";
}int main(){
    ios::sync_with_stdio(0),cin.tie(0);
    for(cin >> T;T --;) los();
}