I. Lulu And The Magical Array

#include <algorithm>
#include <queue>
#include <vector>
#include <set>
#include <iostream>
#include <map>
#include <iomanip>

using namespace std;

#define ll long long
#define fastio ios::sync_with_stdio(false), cin.tie(0);
#define pll pair<ll, ll>
#define pdd pair<double, double>
#define F first
#define S second
#define pb push_back
#define ppb pop_back
#define mkp make_pair
#define sz(a) (ll) a.size()
#define all(x) x.begin(), x.end()
#define rep(i, n) for (ll i = 1; i <= n; i++)
#define lowbit(x) x &(-x)

ll N;

// l is 0 r is 1
struct Node{
  ll x;
  Node *l, *r;
  Node(){x = 0, l = r = NULL;};
};

void build(Node *v, ll x, ll level){
  v->x++;
  if(level == -1) return;
  if(x & (1ll << level)){
    if(v->r == NULL) v->r = new Node();
    build(v->r, x, level - 1);
  }
  else{
    if(v->l == NULL) v->l = new Node();
    build(v->l, x, level - 1);
  }
}

ll DFS(ll x, Node *v, ll level, ll flag){
  ll rev = 0;
  if(level == -1) return 0ll;
  if(x & (1ll << level)){
    // cerr << (v->r != NULL) << " " << (v->r->x > flag) << endl;
    if(v->r != NULL and v->r->x > flag){
      rev += DFS(x, v->r, level - 1, flag);
    }
    else{
      // cerr << x << " 0 " << level << endl;
      rev += (1ll << level);
      rev += DFS(x, v->l, level - 1, 0);
    }
  }
  else{
    if(v->l != NULL and v->l->x > flag){
      rev += DFS(x, v->l, level - 1, flag);
    }
    else{
      // cerr << x << " 1 " << level << endl;
      rev += (1ll << level);
      rev += DFS(x, v->r, level - 1, 0);
    }
  }
  return rev;
}

void solve(){
  cin >> N;
  vector<ll> a;
  ll x;
  ll ans = (1ll << 31);
  for(ll i = 2; i <= N; i++){
    cout << "? " << 1 << " " << i << '\n';
    cout << flush;
    cin >> x;
    a.push_back(x);
    ans = min(ans, x);
  }
  if(N == 2){
    cout << "! " << ans << '\n';
    cout << flush << '\n';
    return;
  }
  Node *root = new Node();
  for(ll i = 0; i < a.size(); ++i){
    build(root, a[i], 30);
  }
  for(ll i = 0; i < a.size(); ++i){
    ll res = DFS(a[i], root, 30, 1);
    ans = min(ans, res);
  }
  cout << "! " << ans << '\n';
  cout << flush << '\n';
}

signed main() {
  fastio ll T = 1;
  cin >> T;
  for (ll i = 1; i <= T; i++) {
    solve();
  }
  return 0;
}