#include<bits/stdc++.h>
using namespace std;
const int N=3e6+5;
int T,n,p[N],f[N],s[N],m,ls[N];
bool t[N];
void solve(){
	scanf("%d",&n),m=0;
	for(int i=1;i<=n;++i)scanf("%d",&p[i]);
	for(int r=n,l;r;r=l-1){
		l=p[r],t[l]=true;
		for(int i=l;i<r;++i)if(p[i]<l)return puts("-1"),void();
		for(int i=l+1,o=1;i<=r;++i){
			f[i]=i-o;
			if(p[i]==l)t[i]=true,o=i-l+1;
			else if(i-p[i]==f[i]-p[f[i]])t[i]=false;
			else return puts("-1"),void();
		}
		bool fg=false;
		s[l]=m?ls[1]:0;
		for(int i=l+1;i<=r;++i){
			s[i]=s[f[i]]+t[i];
			int u=i-l+1>m?0:ls[i-l+1];
			if(s[i]>u)fg=true;
			else if(!fg&&s[i]<u){
				if(t[i])s[i]=u;
				else{
					int j=i-1;
					while(!t[j])--j;
					++s[j],i=j,fg=true;
				}
			}
		}
		if(!fg&&r-l+1<m){
			int j=r;
			while(!t[j])--j;
			++s[j];
			for(int i=j+1;i<=r;++i)s[i]=s[f[i]]+t[i];
		}
		m=r-l+1;
		for(int i=l;i<=r;++i)ls[i-l+1]=s[i];
	}
	for(int i=1;i<=n;++i)printf("%d%c",s[i]+1," \n"[i==n]);
}
int main(){
	scanf("%d",&T);
	while(T--)solve();
	return 0;
}