#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define eb emplace_back
//mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
#define mod 998244353
#define ll long long
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f3f3f
inline int read()
{
	char ch=getchar(); int nega=1; while(!isdigit(ch)) {if(ch=='-') nega=-1; ch=getchar();}
	int ans=0; while(isdigit(ch)) {ans=ans*10+ch-48;ch=getchar();}
	if(nega==-1) return -ans;
	return ans;
}
void print(vector<int> x){for(int i=0;i<(int)x.size();i++) printf("%d%c",x[i]," \n"[i==(int)x.size()-1]);}
#define N 3000005
int tw[N],a[N],ans[N],top[N],fa[N],n;
int find(int u) {return fa[u]==u?u:fa[u]=find(fa[u]);}
vector<int> G[N];
void work()
{
	n=read();
	for(int i=1;i<=n;i++) a[i]=read();
	for(int i=1;i<=n;i++) fa[i]=i,ans[i]=tw[i]=1;
	int lstlen=0;
	for(int t=n;t>=1;)
	{
		for(int j=a[t];j<=t;j++) top[j]=a[t];
		// i=a[i]-1;
		int i=a[t],j=i+1,k=i;
		if(a[i]!=i)
		{
			cout<<"-1\n";
			return ;
		}
		while(j<=t)
		{
			if(a[j]==i)
			{
				// ans[j]=ans[k]+1;
				k=i;
				j++;
			}
			else if(a[j]==a[k]+(j-k))
			{
				// ans[j]=ans[k];
				fa[find(j)]=find(k);
				k++;
				j++;
			}
			else
			{
				cout<<"-1\n";
				return ;
			}
		}
		int addpos=-1;
		int ok=0;
		i=a[t],j=i+1,k=i;
		if(t!=n)
		{
			ans[i]=max(ans[i],ans[t+1]);
		}
		while(j<=t)
		{
			if(a[j]==i)
			{
				ans[find(j)]=max(ans[find(j)],ans[find(k)]+1);
				if(!ok)
				{
					if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1) ans[find(j)]=max(ans[find(j)],ans[find(t+j-a[t]+1)]);
				}
				if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1)
				{
					if(ans[find(j)]>ans[find(t+j-a[t]+1)]) ok=1;
				}
				else ok=1;
				k=i;
				j++;
			}
			else if(a[j]==a[k]+(j-k))
			{
				// ans[j]=ans[k];
				// fa[find(j)]=find(k);
				if(!ok)
				{
					if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1)
					{
						if(ans[find(t+j-a[t]+1)]>ans[find(j)])
						{
							for(int c=j;c>=a[t];c--) if(find(c)==c)
							{
								addpos=c;
								break;
							}
							ok=1;
							break;
						}
					}
				}
				if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1)
				{
					if(ans[find(j)]>ans[find(t+j-a[t]+1)]) ok=1;
				}
				else ok=1;
				k++;
				j++;
			}
		}
		if(ok==0&&t-a[t]+1<lstlen)
		{
			for(int c=t;c>=a[t];c--)
			{
				if(find(c)==c)
				{
					addpos=c;
					break;
				}
			}
		}
		if(addpos!=-1)
		{
			for(int c=a[t];c<=t;c++) ans[c]=1;
			int ok=0;
			i=a[t],j=i+1,k=i;
			if(t!=n)
			{
				ans[i]=max(ans[i],ans[t+1]);
			}
			if(addpos==i) ans[i]++;
			if(t==n||ans[i]>ans[t+1]) ok=1;
			while(j<=t)
			{
				if(a[j]==i)
				{
					ans[find(j)]=max(ans[find(j)],ans[find(k)]+1);
					if(!ok)
					{
						if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1) ans[find(j)]=max(ans[find(j)],ans[find(t+j-a[t]+1)]);
					}
					if(j==addpos) ans[j]++;
					if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1)
					{
						if(ans[find(j)]>ans[find(t+j-a[t]+1)]) ok=1;
					}
					else ok=1;
					k=i;
					j++;
				}
				else if(a[j]==a[k]+(j-k))
				{
					// ans[j]=ans[k];
					// fa[find(j)]=find(k);
					if(j==addpos) ans[j]++;
					if(t+j-a[t]+1<=n&&top[t+j-a[t]+1]==t+1)
					{
						if(ans[find(j)]>ans[find(t+j-a[t]+1)]) ok=1;
					}
					else ok=1;
					k++;
					j++;
				}
			}
		}
		lstlen=t-a[t]+1;
		t=a[t]-1;
	}
	// for(int i=1;i<=n;i++) printf("%d%c",top[i]," \n"[i==n]);
	for(int i=1;i<=n;i++) printf("%d%c",ans[find(i)]," \n"[i==n]);
}
signed main()
{
	int T=read(); while(T--) work();
	return 0;
}