#include <bits/stdc++.h>
#define int long long
using namespace std;
void solve() {
int n;
cin>>n;
vector<int> v(n+1);
int sum=(n*(n+1))/2;
map<int,int> mp;
for(int i=1;i<=n;i++){
mp[i*i]=1;
}
if(mp.find(sum)!=mp.end()){
cout<<-1<<endl;
return;
}
for(int i=1;i<=n;i++){
v[i]=i;
}
sum=0;
for(int i=1;i<n;i++){
sum+=v[i];
if(mp.find(sum)!=mp.end()){
int a=v[i],b=v[i+1];
swap(v[i],v[i+1]);
sum-=a;
sum+=b;
}
}
for(int i=1;i<=n;i++){
cout<<v[i]<<" ";
}
cout<<endl;
}
signed main() {
int t;
cin >> t;
while (t--) {
solve();
}
return 0;
}
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