Problem: Let's call two numbers similar if their binary representations contain the same number of digits equal to 1. For example:

  * 2 and 4 are similar (binary representations are 10 and 100); 
  * 1337 and 4213 are similar (binary representations are 10100111001 and 1000001110101); 
  * 3 and 2 are not similar (binary representations are 11 and 10); 
  * 42 and 13 are similar (binary representations are 101010 and 1101). 



You are given an array of n integers a_1, a_2, ..., a_n. You may choose a non-negative integer x, and then get another array of n integers b_1, b_2, ..., b_n, where b_i = a_i ⊕ x (⊕ denotes bitwise XOR).

Is it possible to obtain an array b where all numbers are similar to each other?

Input

The first line contains one integer n (2 ≤ n ≤ 100).

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2^{30} - 1).

Output

If it is impossible to choose x so that all elements in the resulting array are similar to each other, print one integer -1.

Otherwise, print any non-negative integer not exceeding 2^{30} - 1 that can be used as x so that all elements in the resulting array are similar.

Examples

Input


2
7 2


Output


1


Input


4
3 17 6 0


Output


5


Input


3
1 2 3


Output


-1


Input


3
43 12 12


Output


1073709057

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("-ffloat-store")
using namespace std;
clock_t time_p = clock();
void aryanc403() {}
const int INF = 0xFFFFFFFFFFFFFFFL;
int seed;
mt19937 rng(seed = chrono::steady_clock::now().time_since_epoch().count());
inline int rnd(int l = 0, int r = INF) {
  return uniform_int_distribution<int>(l, r)(rng);
}
class CMP {
 public:
  bool operator()(pair<int, int> a, pair<int, int> b) {
    return !(a.first < b.first || (a.first == b.first && a.second <= b.second));
  }
};
void add(map<int, int> &m, int x, int cnt = 1) {
  auto jt = m.find(x);
  if (jt == m.end())
    m.insert({x, cnt});
  else
    jt->second += cnt;
}
void del(map<int, int> &m, int x, int cnt = 1) {
  auto jt = m.find(x);
  if (jt->second <= cnt)
    m.erase(jt);
  else
    jt->second -= cnt;
}
bool cmp(const pair<int, int> &a, const pair<int, int> &b) {
  return a.first < b.first || (a.first == b.first && a.second < b.second);
}
const int mod = 1000000007L;
const int N = 15;
int T, n, i, j, k, in, cnt, l, r, u, v, x, y;
int m;
string s;
vector<int> a;
template <class T>
void makeUnq(vector<T> &a) {
  sort(begin(a), end(a));
  a.resize(unique(begin(a), end(a)) - a.begin());
}
void com(vector<int> &a, map<vector<int>, int> &ans) {
  const int lim = (1LL << N) - 1;
  for (int i = 0; i <= lim; ++i) {
    vector<int> b;
    for (auto x : a) b.push_back(__builtin_popcount((x ^ i) & lim));
    ans[b] = i;
  }
}
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  {
    cin >> n;
    a.clear();
    a.reserve(n);
    for (i = 0; i < (n); ++i) {
      cin >> in;
      a.push_back(in);
    }
    makeUnq(a);
    n = (int)(a).size();
    map<vector<int>, int> fh, sh;
    com(a, fh);
    for (auto &x : a) x /= 1LL << N;
    com(a, sh);
    for (auto &v : fh) {
      int mx = 0;
      for (auto x : v.first) mx = max(mx, x);
      vector<int> b;
      for (int i = mx; i <= 2 * N; ++i) {
        b.clear();
        for (auto x : v.first) b.push_back(i - x);
        auto it = sh.find(b);
        if (it != sh.end()) {
          cout << (it->second) * (1LL << N) + v.second << "\n";
          exit(0);
        }
      }
    }
    cout << -1 << "\n";
  }
  aryanc403();
  return 0;
}