cf-1017.cpp

#include <bits/stdc++.h>
using namespace std;
#define ll long long

void solve() {
    ll x;
    cin >> x;
    vector<ll> v(x);
    for (int i = 0; i < x; i++) {
        cin >> v[i];
    }

    // Store 32-bit binary strings
    vector<string> store;
    for (int i = 0; i < x; i++) {
        string s = "";
        for (int j = 31; j >= 0; j--) {
            s += ((v[i] >> j) & 1) ? '1' : '0';
        }
        store.push_back(s);
    }

    vector<bool> eliminated(x, false); 
    int remaining = x;

    for (int i = 31; i >=0; i--) {
        int zeroCount = 0, oneCount = 0;
        for (int j = 0; j < x; j++) {
            if (store[j][i] == '0') zeroCount++;
            else oneCount++;
        }
        char majority = (zeroCount > oneCount) ? '0' : '1';
        int flg=0;
        for(int j=0;j<x;j++){
            if(!eliminated[j] && store[j][i]!=majority){
                flg=1;
            }
        }
        int count=0,count1=0;
        for(int j=0;j<x;j++){
            if(!eliminated[j] && store[j][i]==majority){
                count++;
            }
        }
        for(int j=0;j<x;j++){
            if(eliminated[j]){
                count1++;
            }
        }
        cout<<count+count1<<" ";
        if(flg==0 || (count1+count==x)) continue;
        for (int j = 0; j < x; j++) {
            if (eliminated[j]) continue;
            if (store[j][i] == majority) {
                eliminated[j] = true;
                remaining--;
            }
        }

    }

    ll val = -1;
    for (int i = 0; i < x; i++) {
        if (!eliminated[i]) {
            val = v[i];
            break;
        }
    }

   

    cout << val << " ";

    ll ans = 0;
    for (int i = 0; i < x; i++) {
        ans += (v[i] ^ val);
    }

    cout << ans << endl;
}

int main() {
    ll t;
    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}