#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using i64 = int64_t;
template <class T>
bool set_max(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool set_min(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename T>
string to_string(T v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const int inf = (int)1e9 + 5;
const int MOD = 1e9 + 7;
const double eps = 1e-6;
void run_case() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int &x : a) {
    cin >> x;
  }
  vector<tuple<int, int, int>> v(n);
  i64 ans = 0;
  int mask = 0;
  for (int bit = 0; bit < 30; bit++) {
    for (int i = 0; i < n; i++) {
      v[i] = make_tuple(a[i] >> (1 + bit), i, (a[i] >> bit) & 1);
    }
    sort(v.begin(), v.end());
    i64 inv0 = 0, inv1 = 0;
    int begin = 0;
    while (begin < n) {
      int end = begin;
      while (end + 1 < n && get<0>(v[end + 1]) == get<0>(v[end])) end++;
      int k0 = 0, k1 = 0;
      for (int i = begin; i <= end; i++) {
        if (get<2>(v[i])) {
          inv1 += k0;
          k1++;
        } else {
          inv0 += k1;
          k0++;
        }
      }
      begin = end + 1;
    }
    if (inv0 <= inv1) {
      ans += inv0;
    } else {
      ans += inv1;
      mask += 1 << bit;
    }
  }
  cout << ans << " " << mask << "\n";
}
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  int test_case = 1;
  while (test_case--) {
    run_case();
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

You are given an array a consisting of n non-negative integers. You have to choose a non-negative integer x and form a new array b of size n according to the following rule: for all i from 1 to n, b_i = a_i ⊕ x (⊕ denotes the operation [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR)).

An inversion in the b array is a pair of integers i and j such that 1 ≤ i < j ≤ n and b_i > b_j.

You should choose x in such a way that the number of inversions in b is minimized. If there are several options for x — output the smallest one.

Input

First line contains a single integer n (1 ≤ n ≤ 3 ⋅ 10^5) — the number of elements in a.

Second line contains n space-separated integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Output two integers: the minimum possible number of inversions in b, and the minimum possible value of x, which achieves those number of inversions.

Examples

Input


4
0 1 3 2


Output


1 0


Input


9
10 7 9 10 7 5 5 3 5


Output


4 14


Input


3
8 10 3


Output


0 8

Note

In the first sample it is optimal to leave the array as it is by choosing x = 0.

In the second sample the selection of x = 14 results in b: [4, 9, 7, 4, 9, 11, 11, 13, 11]. It has 4 inversions:

  * i = 2, j = 3; 
  * i = 2, j = 4; 
  * i = 3, j = 4; 
  * i = 8, j = 9. 



In the third sample the selection of x = 8 results in b: [0, 2, 11]. It has no inversions.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using i64 = int64_t;
template <class T>
bool set_max(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool set_min(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename T>
string to_string(T v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const int inf = (int)1e9 + 5;
const int MOD = 1e9 + 7;
const double eps = 1e-6;
void run_case() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int &x : a) {
    cin >> x;
  }
  vector<tuple<int, int, int>> v(n);
  i64 ans = 0;
  int mask = 0;
  for (int bit = 0; bit < 30; bit++) {
    for (int i = 0; i < n; i++) {
      v[i] = make_tuple(a[i] >> (1 + bit), i, (a[i] >> bit) & 1);
    }
    sort(v.begin(), v.end());
    i64 inv0 = 0, inv1 = 0;
    int begin = 0;
    while (begin < n) {
      int end = begin;
      while (end + 1 < n && get<0>(v[end + 1]) == get<0>(v[end])) end++;
      int k0 = 0, k1 = 0;
      for (int i = begin; i <= end; i++) {
        if (get<2>(v[i])) {
          inv1 += k0;
          k1++;
        } else {
          inv0 += k1;
          k0++;
        }
      }
      begin = end + 1;
    }
    if (inv0 <= inv1) {
      ans += inv0;
    } else {
      ans += inv1;
      mask += 1 << bit;
    }
  }
  cout << ans << " " << mask << "\n";
}
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  int test_case = 1;
  while (test_case--) {
    run_case();
  }
}

```