#include<bits/stdc++.h>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/assoc_container.hpp>
#define ll long long
//#define int long long
using namespace std;

const int maxn = 310000;

signed main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	int Tcase; cin>>Tcase;
	while(Tcase--)
	{
		int n; cin>>n;
		vector<int>b(n+5);
		for(int i=1;i<=n;i++) cin>>b[i];
		
		{
			int ok=1;
			for(int i=1;i<=n;i++) if(b[i]!=i) ok=0;
			if(ok)
			{
				for(int i=1;i<=n;i++) cout<<1<<" \n"[i==n];
				continue;
			}
		}
		{
			int ok=1;
			if(b[1]==n+1) ok=0;
			for(int i=1;i<=n;i++) if(b[i]<i) ok=0;
			if(ok==0)
			{
				cout<<"-1\n";
				continue;
			}
		}
		
		vector<int>nex(n+5);
		int fir=b[1];
		for(int i=1;i<=n;i++)
		{
			if(b[i+1]>n)
			{
				nex[i]=n+1;
				break;
			}
			if(b[i+1]<=n && b[i]!=b[i+1])
				nex[i]=b[i+1];
		}
		
		vector<int>v(n+5); v[fir]=1;
		for(int i=1;i<=n;i++) if(nex[i])
			v[i]=v[nex[i]]=1;
		
		vector<int>flag(n+5);
		flag[1]++,flag[fir+1]--;
		if(nex[fir]) flag[fir]--,flag[fir+1]++;
		for(int i=1;i<=n;i++) if(nex[i])
		{
			flag[i]++;
			flag[nex[i]+1]--;
			if(nex[nex[i]]) flag[nex[i]]--,flag[nex[i]+1]++;
		}
		
		int cnt=0;
		for(int i=1;i<=n;i++)
		{
			flag[i]+=flag[i-1];
			cnt=max(cnt, flag[i]+(v[i]==0) );
		}
		
		vector<int>a(n+5);
		set< pair<int,int> >S;
		
		a[fir]=1; S.emplace(fir,a[fir]);
		for(int i=2;i<=cnt;i++) S.emplace(0,i);
		for(int i=1;i<=n;i++)
		{
			if(!a[i])
			{
				auto it=S.begin();
				if( it->first <i )
				{
					int c=it->second;
					S.erase(it);
					a[i]=c;
					S.emplace( i,c );
				}
				else
				{
					a[i]=++cnt;
					S.emplace( i,a[i] );
				}
			}
			
			if(nex[i])
			{
				auto it=S.find( make_pair(i,a[i]) );
				S.erase(it);
				S.emplace( nex[i],a[i] );
				a[nex[i]]=a[i];
			}
		}
		
		vector<int>num(cnt+5);
		int ok=1;
		for(int i=1,j=0,now=0;i<=n;i++)
		{
			while(j<b[i] && j<n)
			{
				j++;
				if(num[a[j]]==0) now++;
				num[a[j]]++;
			}
			if( b[i]<=n && now!=cnt ) ok=0;
			if( b[i]>n && now>cnt ) ok=0;
			
			num[a[i]]--;
			if(num[a[i]]==0) now--;
		}
		if(ok)
		{
			for(int i=1;i<=n;i++) cout<<a[i]<<" \n"[i==n];
		}
		else
		{
			cout<<"-1\n";
		}
	}
	
	return 0;
}