#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int fx[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
const int fxx[8][2] = {{0, 1}, {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
struct node {
  long long sz, x, left, right;
  node() {
    sz = 0, x = 0;
    left = right = -1;
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = int(0); i < int(n); i++) cin >> a[i];
  vector<node> tr(1);
  for (int i = n - 1; i >= 0; i--) {
    int cur = 0;
    for (int j = 30; j >= 0; j--) {
      if (a[i] & (1 << j)) {
        if (tr[cur].right == -1) {
          tr[cur].right = tr.size();
          tr.push_back({});
        }
        int nxt = tr[cur].right;
        tr[nxt].x += tr[cur].left == -1 ? 0 : tr[tr[cur].left].sz;
        tr[nxt].sz += 1;
        cur = nxt;
      } else {
        if (tr[cur].left == -1) {
          tr[cur].left = tr.size();
          tr.push_back({});
        }
        int nxt = tr[cur].left;
        tr[nxt].x += tr[cur].right == -1 ? 0 : tr[tr[cur].right].sz;
        tr[nxt].sz += 1;
        cur = nxt;
      }
    }
  }
  long long invb = 0, x = 0;
  queue<int> q;
  q.push(0);
  while (!q.empty()) {
    long long z = 0, o = 0;
    int levelsz = q.size();
    for (int i = int(0); i < int(levelsz); i++) {
      int u = q.front();
      q.pop();
      o += tr[u].left == -1 ? 0 : tr[tr[u].left].x;
      z += tr[u].right == -1 ? 0 : tr[tr[u].right].x;
      if (tr[u].left != -1) q.push(tr[u].left);
      if (tr[u].right != -1) q.push(tr[u].right);
    }
    x <<= 1;
    if (z <= o)
      x += 0;
    else
      x += 1;
    invb += min(z, o);
  }
  x >>= 1;
  cout << invb << " " << x << "\n";
  return 0;
}

### Prompt

Please create a solution in cpp 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;
void err(istream_iterator<string> it) { cerr << endl; }
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int fx[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
const int fxx[8][2] = {{0, 1}, {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
struct node {
  long long sz, x, left, right;
  node() {
    sz = 0, x = 0;
    left = right = -1;
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = int(0); i < int(n); i++) cin >> a[i];
  vector<node> tr(1);
  for (int i = n - 1; i >= 0; i--) {
    int cur = 0;
    for (int j = 30; j >= 0; j--) {
      if (a[i] & (1 << j)) {
        if (tr[cur].right == -1) {
          tr[cur].right = tr.size();
          tr.push_back({});
        }
        int nxt = tr[cur].right;
        tr[nxt].x += tr[cur].left == -1 ? 0 : tr[tr[cur].left].sz;
        tr[nxt].sz += 1;
        cur = nxt;
      } else {
        if (tr[cur].left == -1) {
          tr[cur].left = tr.size();
          tr.push_back({});
        }
        int nxt = tr[cur].left;
        tr[nxt].x += tr[cur].right == -1 ? 0 : tr[tr[cur].right].sz;
        tr[nxt].sz += 1;
        cur = nxt;
      }
    }
  }
  long long invb = 0, x = 0;
  queue<int> q;
  q.push(0);
  while (!q.empty()) {
    long long z = 0, o = 0;
    int levelsz = q.size();
    for (int i = int(0); i < int(levelsz); i++) {
      int u = q.front();
      q.pop();
      o += tr[u].left == -1 ? 0 : tr[tr[u].left].x;
      z += tr[u].right == -1 ? 0 : tr[tr[u].right].x;
      if (tr[u].left != -1) q.push(tr[u].left);
      if (tr[u].right != -1) q.push(tr[u].right);
    }
    x <<= 1;
    if (z <= o)
      x += 0;
    else
      x += 1;
    invb += min(z, o);
  }
  x >>= 1;
  cout << invb << " " << x << "\n";
  return 0;
}

```