#include<bits/stdc++.h>
using namespace std;
bool check(int k,int arr[],int n){
int a[n];
for(int i=0;i<n;i++){
a[i] = (arr[i]^k);
}
sort(a,a+n);
for(int i=0;i<n;i++){
if(a[i]!=arr[i])
return false;
}
return true;
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int arr[n];
for(int i=0;i<n;i++)
cin>>arr[i];
sort(arr,arr+n);
int ans =INT_MAX;
int l=1,r=1024;
while(l<=r){
int mid = l + ((r-l)/2);
if(check(mid,arr,n)){
ans = min(ans,mid);
r=mid-1;
}
else
l=mid+1;
}
if(ans==INT_MAX)
cout<<-1<<"\n";
else
cout<<ans<<"\n";
}
}
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