#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
vector<string> vec_splitter(string s) {
  s += ',';
  vector<string> res;
  while (!s.empty()) {
    res.push_back(s.substr(0, s.find(',')));
    s = s.substr(s.find(',') + 1);
  }
  return res;
}
void debug_out(vector<string> __attribute__((unused)) args,
               __attribute__((unused)) long long int idx,
               __attribute__((unused)) long long int LINE_NUM) {
  cout << '\n';
}
template <typename Head, typename... Tail>
void debug_out(vector<string> args, long long int idx, long long int LINE_NUM,
               Head H, Tail... T) {
  if (idx > 0)
    cout << ", ";
  else
    cout << "Line(" << LINE_NUM << ") ";
  stringstream ss;
  ss << H;
  cout << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, LINE_NUM, T...);
}
const long long int mod = 1000000007;
const long long int inf = 1e18;
const long long int N = 1e5 + 5;
class Trie {
 private:
  class Node {
   public:
    Node *nxt[2];
    long long int cnt;
    Node() {
      nxt[0] = nxt[1] = NULL;
      cnt = 0;
    }
  };

 public:
  Node *head;
  long long int lft[40], rght[40];
  Trie() {
    head = new Node();
    memset(lft, 0, sizeof(lft));
    memset(rght, 0, sizeof(rght));
  }
  void insert(long long int x) {
    Node *cur = head;
    for (long long int i = 30; i >= 0; i--) {
      cur->cnt++;
      long long int b = (x >> i) & 1;
      if (b and cur->nxt[0]) {
        lft[i] += cur->nxt[0]->cnt;
      }
      if (!b and cur->nxt[1]) {
        rght[i] += cur->nxt[1]->cnt;
      }
      if (!cur->nxt[b]) {
        cur->nxt[b] = new Node();
      }
      cur = cur->nxt[b];
    }
    cur->cnt++;
  }
};
void HyperBeast() {
  Trie t;
  long long int n;
  cin >> n;
  for (long long int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    t.insert(x);
  }
  long long int inv = 0;
  long long int x = 0;
  for (long long int i = 30; i >= 0; i--) {
    inv += min(t.lft[i], t.rght[i]);
    if (t.rght[i] > t.lft[i]) {
      x += (1LL << i);
    }
  }
  cout << inv << ' ' << x;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int T = 1;
  for (long long int ti = 1; ti <= T; ti++) {
    HyperBeast();
    cout << '\n';
  }
}

### Prompt

In CPP, your task is to solve the following problem:

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>
#pragma GCC optimize("O3")
using namespace std;
vector<string> vec_splitter(string s) {
  s += ',';
  vector<string> res;
  while (!s.empty()) {
    res.push_back(s.substr(0, s.find(',')));
    s = s.substr(s.find(',') + 1);
  }
  return res;
}
void debug_out(vector<string> __attribute__((unused)) args,
               __attribute__((unused)) long long int idx,
               __attribute__((unused)) long long int LINE_NUM) {
  cout << '\n';
}
template <typename Head, typename... Tail>
void debug_out(vector<string> args, long long int idx, long long int LINE_NUM,
               Head H, Tail... T) {
  if (idx > 0)
    cout << ", ";
  else
    cout << "Line(" << LINE_NUM << ") ";
  stringstream ss;
  ss << H;
  cout << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, LINE_NUM, T...);
}
const long long int mod = 1000000007;
const long long int inf = 1e18;
const long long int N = 1e5 + 5;
class Trie {
 private:
  class Node {
   public:
    Node *nxt[2];
    long long int cnt;
    Node() {
      nxt[0] = nxt[1] = NULL;
      cnt = 0;
    }
  };

 public:
  Node *head;
  long long int lft[40], rght[40];
  Trie() {
    head = new Node();
    memset(lft, 0, sizeof(lft));
    memset(rght, 0, sizeof(rght));
  }
  void insert(long long int x) {
    Node *cur = head;
    for (long long int i = 30; i >= 0; i--) {
      cur->cnt++;
      long long int b = (x >> i) & 1;
      if (b and cur->nxt[0]) {
        lft[i] += cur->nxt[0]->cnt;
      }
      if (!b and cur->nxt[1]) {
        rght[i] += cur->nxt[1]->cnt;
      }
      if (!cur->nxt[b]) {
        cur->nxt[b] = new Node();
      }
      cur = cur->nxt[b];
    }
    cur->cnt++;
  }
};
void HyperBeast() {
  Trie t;
  long long int n;
  cin >> n;
  for (long long int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    t.insert(x);
  }
  long long int inv = 0;
  long long int x = 0;
  for (long long int i = 30; i >= 0; i--) {
    inv += min(t.lft[i], t.rght[i]);
    if (t.rght[i] > t.lft[i]) {
      x += (1LL << i);
    }
  }
  cout << inv << ' ' << x;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int T = 1;
  for (long long int ti = 1; ti <= T; ti++) {
    HyperBeast();
    cout << '\n';
  }
}

```