#include<bits/stdc++.h>
using namespace std;
const int MAXN=2e5+10;
template <typename _Tp>
inline _Tp read(_Tp &x) {
	char ch = getchar(), sgn = 0; x = 0;
	while (ch ^ '-' && !isdigit(ch)) ch = getchar();
	if (ch == '-') ch = getchar(), sgn = 1;
	while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
	if (sgn) x = -x;
	return x;
}
const int N=3e6+10;
int p[N],a[N],b[N],ans[N],s[N];
int n,T,len,flag;
void solve(int l,int r){
	int k=l;
	if (p[l]!=l){
		flag=0; return;
	}
	for (int i=l+1;i<=r;i++) 
	if (p[i]==l){
		a[i]=k;
		b[i]=1;
		k=l;
	}else{
		if (p[i]<l) {flag=0;return;}
		if ((i-p[i])!=(k-p[k])) {flag=0;return;}
		a[i]=k;
		b[i]=0;
		k++;
	}
	a[l]=l; b[l]=1;
	ans[l]=(len?s[1]:1);
	bool OK=0;
	for (int i=l+1;i<=r;i++){
		if (i>len||OK){
			if (b[i]) ans[i]=ans[a[i]]+1; else ans[i]=ans[a[i]];
		}else{
			if (b[i]){
				ans[i]=ans[a[i]]+1;
				if (ans[i]>s[i-l+1]) OK=1;
				else if (ans[i]<s[i-l+1]){
					ans[i]=s[i-l+1];
				}
			}else{
				ans[i]=ans[a[i]];
				if (ans[i]>s[i-l+1]) OK=1;
				else if (ans[i]<s[i-l+1]){
					for (int j=i-1;j>=1;j--) if (b[j]){
						ans[j]++;
						i=j; OK=1; break;
					}
				}
			}
		}
	}
	if ((r-l+1<len)&&!OK){
		for (int j=r;j>=l;j--) if (b[j]){
			ans[j]++;
			for (int k=j+1;k<=r;k++) if (b[k]) ans[k]=ans[a[k]]+1; else ans[k]=ans[a[k]];
			break;
		}
	}
	for (int i=l;i<=r;i++) s[i-l+1]=ans[i];
	len=r-l+1;
}
int main(){
	scanf("%d",&T);
	while (T--){
		scanf("%d",&n);
		flag=1;
		for (int i=1;i<=n;i++) read(p[i]);
		len=0;
		int t=n;
		while (t){
			solve(p[t],t);
			if (!flag) break;
			t=p[t]-1;
		}
		if (flag){
			for (int i=1;i<=n;i++) printf("%d ",ans[i]);
			putchar('\n');
		}else puts("-1");
	}
}