// what is matter? never mind. 
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
#define ull unsigned long long
//#define int __int128
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	if(f)x=-x;return x;
}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 3000005
#define inf 0x3f3f3f3f

int n,p[maxn],a[maxn],bo[maxn],res[maxn];
int len,s[maxn];

bool work()
{
	n=read();
	For(i,1,n)p[i]=read(),bo[i]=0;
	len=0,s[1]=1;
	for(int l=p[n],r=n;r>=1;r=l-1,l=p[r]){
		int k=l;
		a[l]=k,bo[l]=1;
		if(p[l]!=l)return 0;
		For(i,l+1,r){
			if(p[i]==l) bo[i]=1,a[i]=k,k=l;
			else {
				if(i-p[i]!=k-p[k])return 0;
				a[i]=k,bo[i]=0,++k;
			}
		}
		bool big=0;
		res[l]=s[1];
		For(i,l+1,r){
			if(bo[i]){
				res[i]=res[a[i]]+1;
				if(res[i]>s[i-l+1])big=1;
				if(!big && i-l+1<=len && res[i]<s[i-l+1])res[i]=s[i-l+1];
			}else{
				res[i]=res[a[i]];
				if(res[i]>s[i-l+1])big=1;
				if(!big && i-l+1<=len && res[i]<s[i-l+1]){
					Rep(j,i-1,l)
						if(bo[j]){
							++res[j],i=j,big=1;
							break;
						}
				}
			}
		}
		if(!big && r-l+1<len) {
			Rep(i,r,l)
				if(bo[i]){
					++res[i];
					For(j,i+1,r)res[j]=res[a[j]]+bo[j];
					break;
				}
		}
		len=r-l+1;
		For(i,1,len) s[i]=res[i+l-1];
	}
	For(i,1,n)printf("%d ",res[i]);puts("");
	return 1;
}

signed main()
{
	int T=read();
	while(T--)if(!work())puts("-1");
	return 0;
}

/*
6
3
1 1 1
3
1 1 2
3
1 1 3
3
1 2 1
3
1 2 2
3
1 2 3
*/