#include <bits/stdc++.h>
using namespace std;
namespace IO {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  if (s.size()) {
    setIn(s + ".inp");
    setOut(s + ".out");
  } else {
  }
}
}  // namespace IO
using namespace IO;
namespace Function {
template <typename T1, typename T2>
void amax(T1 &a, T2 b) {
  assert(!(typeid(a).name() == typeid(int).name() &&
           typeid(b).name() == typeid(long long).name()));
  if (a < b) a = b;
}
template <typename T1, typename T2>
void amin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T>
void compress(T &a) {
  sort(a.begin(), a.end());
  a.resize(unique(a.begin(), a.end()) - a.begin());
}
template <typename T1, typename T2, typename T3>
int position(T1 Begin, T2 End, T3 val, bool type = 0) {
  if (type == 0) {
    return lower_bound(Begin, End, val) - Begin;
  }
  return upper_bound(Begin, End, val) - Begin;
}
template <typename T>
long long sqr(T x) {
  return 1LL * x * x;
}
template <typename T1, typename T2>
long long GCD(T1 a, T2 b) {
  return b == 0 ? a : GCD(b, a % b);
}
template <typename T1, typename T2>
long long LCM(T1 a, T2 b) {
  return 1LL * a / GCD(a, b) * b;
}
}  // namespace Function
using namespace Function;
namespace Output {
void print(int x) { cout << x << "\n"; }
void print(unsigned int x) { cout << x << "\n"; }
void print(long unsigned int x) { cout << x << "\n"; }
void print(long long x) { cout << x << "\n"; }
void print(unsigned long long x) { cout << x << "\n"; }
void print(float x) { cout << x << "\n"; }
void print(double x) { cout << x << "\n"; }
void print(long double x) { cout << x << "\n"; }
void print(char x) { cout << x << "\n"; }
void print(char *x) { cout << x << "\n"; }
void print(unsigned char x) { cout << x << "\n"; }
void print(const char *x) { cout << x << "\n"; }
void print(string x) { cout << x << "\n"; }
void print(bool x) { cout << x << "\n"; }
template <class T, class... Ts>
void print(T t, Ts... ts) {
  cout << t << " ";
  print(ts...);
}
template <typename T1, typename T2>
void print(pair<T1, T2> a) {
  print(a.first, a.second);
}
template <typename T>
void print(T a) {
  for (auto it : a) {
    print(it);
  }
}
template <class T, class... Ts>
void prine(T t, Ts... ts) {
  print(t, ts...);
  exit(0);
}
}  // namespace Output
using namespace Output;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};
const int INF = 1e9;
const long long INFL = 1e18;
const int MOD = 1e9 + 7;
const int N = 3e5 + 10;
int get_bit(int x, int pos) { return (x >> pos) & 1; }
long long x[40], y[40];
void calc(vector<int> a, int pos) {
  if (pos == -1 || (int)a.size() < 2) {
    return;
  }
  vector<int> on, off;
  for (int i : a) {
    if (get_bit(i, pos) == 1) {
      on.push_back(i);
      x[pos] += off.size();
    } else {
      off.push_back(i);
      y[pos] += on.size();
    }
  }
  calc(on, pos - 1);
  calc(off, pos - 1);
}
int main() {
  setIO();
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  calc(a, 30);
  int cur = 1;
  int res2 = 0;
  long long res1 = 0;
  for (int i = 0; i < 31; i++) {
    if (x[i] < y[i]) {
      res2 += (1 << i);
      res1 += x[i];
    } else {
      res1 += y[i];
    }
  }
  print(res1, res2);
  return 0;
}

### Prompt

Please formulate a CPP solution to 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>
using namespace std;
namespace IO {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  if (s.size()) {
    setIn(s + ".inp");
    setOut(s + ".out");
  } else {
  }
}
}  // namespace IO
using namespace IO;
namespace Function {
template <typename T1, typename T2>
void amax(T1 &a, T2 b) {
  assert(!(typeid(a).name() == typeid(int).name() &&
           typeid(b).name() == typeid(long long).name()));
  if (a < b) a = b;
}
template <typename T1, typename T2>
void amin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T>
void compress(T &a) {
  sort(a.begin(), a.end());
  a.resize(unique(a.begin(), a.end()) - a.begin());
}
template <typename T1, typename T2, typename T3>
int position(T1 Begin, T2 End, T3 val, bool type = 0) {
  if (type == 0) {
    return lower_bound(Begin, End, val) - Begin;
  }
  return upper_bound(Begin, End, val) - Begin;
}
template <typename T>
long long sqr(T x) {
  return 1LL * x * x;
}
template <typename T1, typename T2>
long long GCD(T1 a, T2 b) {
  return b == 0 ? a : GCD(b, a % b);
}
template <typename T1, typename T2>
long long LCM(T1 a, T2 b) {
  return 1LL * a / GCD(a, b) * b;
}
}  // namespace Function
using namespace Function;
namespace Output {
void print(int x) { cout << x << "\n"; }
void print(unsigned int x) { cout << x << "\n"; }
void print(long unsigned int x) { cout << x << "\n"; }
void print(long long x) { cout << x << "\n"; }
void print(unsigned long long x) { cout << x << "\n"; }
void print(float x) { cout << x << "\n"; }
void print(double x) { cout << x << "\n"; }
void print(long double x) { cout << x << "\n"; }
void print(char x) { cout << x << "\n"; }
void print(char *x) { cout << x << "\n"; }
void print(unsigned char x) { cout << x << "\n"; }
void print(const char *x) { cout << x << "\n"; }
void print(string x) { cout << x << "\n"; }
void print(bool x) { cout << x << "\n"; }
template <class T, class... Ts>
void print(T t, Ts... ts) {
  cout << t << " ";
  print(ts...);
}
template <typename T1, typename T2>
void print(pair<T1, T2> a) {
  print(a.first, a.second);
}
template <typename T>
void print(T a) {
  for (auto it : a) {
    print(it);
  }
}
template <class T, class... Ts>
void prine(T t, Ts... ts) {
  print(t, ts...);
  exit(0);
}
}  // namespace Output
using namespace Output;
const int dx[] = {1, -1, 0, 0};
const int dy[] = {0, 0, 1, -1};
const int INF = 1e9;
const long long INFL = 1e18;
const int MOD = 1e9 + 7;
const int N = 3e5 + 10;
int get_bit(int x, int pos) { return (x >> pos) & 1; }
long long x[40], y[40];
void calc(vector<int> a, int pos) {
  if (pos == -1 || (int)a.size() < 2) {
    return;
  }
  vector<int> on, off;
  for (int i : a) {
    if (get_bit(i, pos) == 1) {
      on.push_back(i);
      x[pos] += off.size();
    } else {
      off.push_back(i);
      y[pos] += on.size();
    }
  }
  calc(on, pos - 1);
  calc(off, pos - 1);
}
int main() {
  setIO();
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  calc(a, 30);
  int cur = 1;
  int res2 = 0;
  long long res1 = 0;
  for (int i = 0; i < 31; i++) {
    if (x[i] < y[i]) {
      res2 += (1 << i);
      res1 += x[i];
    } else {
      res1 += y[i];
    }
  }
  print(res1, res2);
  return 0;
}

```