#include <bits/stdc++.h>
using namespace std;
long long MOD = 1e9 + 7;
long long INF = 9e18;
vector<string> &split(const std::string &s, char delim, vector<string> &e) {
  stringstream ss(s);
  string item;
  while (getline(ss, item, delim)) e.push_back(item);
  return e;
}
long long Pow(long long a, long long b, long long Mo) {
  long long ans = 1;
  for (; b; b >>= 1, a = a * a % Mo)
    if (b & 1) ans = ans * a % Mo;
  return ans;
}
vector<int> Zfunc(string &s) {
  int n = s.length();
  vector<int> z(n, 0);
  for (int i = 1, l = 0, r = 0; i < n; i++) {
    if (i <= r) z[i] = min(z[i - l], r - i + 1);
    while (i + z[i] < n && s[i + z[i]] == s[z[i]]) z[i]++;
    if (r < i + z[i] - 1) l = i, r = i + z[i] - 1;
  }
  return z;
}
long long solve() { return 0; }
int main(int argc, char const *argv[]) {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  long long n;
  cin >> n;
  std::vector<long long> v(n);
  for (int i = 0; i < n; ++i) {
    cin >> v[i];
  }
  unordered_multiset<int> cp, cn;
  long long base = 0;
  long long S = 0;
  for (int i = 0; i < n; ++i) {
    S += abs(v[i] - (i + 1));
    long long x = v[i] - (i + 1);
    if (x > base) {
      cp.insert(x);
    } else {
      cn.insert(x);
    }
  }
  {}
  long long minS = S, minK = 0;
  for (int i = 1; i < n; ++i) {
    long long ccp = cp.size();
    S += -ccp + (n - ccp);
    base++;
    while (cp.find(base) != cp.end()) {
      cp.erase(cp.find(base));
      cn.insert(base);
    }
    long long insertVal = v[n - i] - (n - i + 1);
    assert(cn.find(insertVal) != cn.end());
    cn.erase(cn.find(insertVal));
    if (insertVal + n > base)
      cp.insert(insertVal + n);
    else
      cn.insert(insertVal + n);
    S -= abs(insertVal - (i));
    S += abs(insertVal - (i) + n);
    if (minS > S) {
      minS = S;
      minK = i;
    }
  }
  cout << minS << ' ' << minK;
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

Some time ago Mister B detected a strange signal from the space, which he started to study.

After some transformation the signal turned out to be a permutation p of length n or its cyclic shift. For the further investigation Mister B need some basis, that's why he decided to choose cyclic shift of this permutation which has the minimum possible deviation.

Let's define the deviation of a permutation p as <image>.

Find a cyclic shift of permutation p with minimum possible deviation. If there are multiple solutions, print any of them.

Let's denote id k (0 ≤ k < n) of a cyclic shift of permutation p as the number of right shifts needed to reach this shift, for example:

  * k = 0: shift p1, p2, ... pn, 
  * k = 1: shift pn, p1, ... pn - 1, 
  * ..., 
  * k = n - 1: shift p2, p3, ... pn, p1. 

Input

First line contains single integer n (2 ≤ n ≤ 106) — the length of the permutation.

The second line contains n space-separated integers p1, p2, ..., pn (1 ≤ pi ≤ n) — the elements of the permutation. It is guaranteed that all elements are distinct.

Output

Print two integers: the minimum deviation of cyclic shifts of permutation p and the id of such shift. If there are multiple solutions, print any of them.

Examples

Input

3
1 2 3


Output

0 0


Input

3
2 3 1


Output

0 1


Input

3
3 2 1


Output

2 1

Note

In the first sample test the given permutation p is the identity permutation, that's why its deviation equals to 0, the shift id equals to 0 as well.

In the second sample test the deviation of p equals to 4, the deviation of the 1-st cyclic shift (1, 2, 3) equals to 0, the deviation of the 2-nd cyclic shift (3, 1, 2) equals to 4, the optimal is the 1-st cyclic shift.

In the third sample test the deviation of p equals to 4, the deviation of the 1-st cyclic shift (1, 3, 2) equals to 2, the deviation of the 2-nd cyclic shift (2, 1, 3) also equals to 2, so the optimal are both 1-st and 2-nd cyclic shifts.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long MOD = 1e9 + 7;
long long INF = 9e18;
vector<string> &split(const std::string &s, char delim, vector<string> &e) {
  stringstream ss(s);
  string item;
  while (getline(ss, item, delim)) e.push_back(item);
  return e;
}
long long Pow(long long a, long long b, long long Mo) {
  long long ans = 1;
  for (; b; b >>= 1, a = a * a % Mo)
    if (b & 1) ans = ans * a % Mo;
  return ans;
}
vector<int> Zfunc(string &s) {
  int n = s.length();
  vector<int> z(n, 0);
  for (int i = 1, l = 0, r = 0; i < n; i++) {
    if (i <= r) z[i] = min(z[i - l], r - i + 1);
    while (i + z[i] < n && s[i + z[i]] == s[z[i]]) z[i]++;
    if (r < i + z[i] - 1) l = i, r = i + z[i] - 1;
  }
  return z;
}
long long solve() { return 0; }
int main(int argc, char const *argv[]) {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  long long n;
  cin >> n;
  std::vector<long long> v(n);
  for (int i = 0; i < n; ++i) {
    cin >> v[i];
  }
  unordered_multiset<int> cp, cn;
  long long base = 0;
  long long S = 0;
  for (int i = 0; i < n; ++i) {
    S += abs(v[i] - (i + 1));
    long long x = v[i] - (i + 1);
    if (x > base) {
      cp.insert(x);
    } else {
      cn.insert(x);
    }
  }
  {}
  long long minS = S, minK = 0;
  for (int i = 1; i < n; ++i) {
    long long ccp = cp.size();
    S += -ccp + (n - ccp);
    base++;
    while (cp.find(base) != cp.end()) {
      cp.erase(cp.find(base));
      cn.insert(base);
    }
    long long insertVal = v[n - i] - (n - i + 1);
    assert(cn.find(insertVal) != cn.end());
    cn.erase(cn.find(insertVal));
    if (insertVal + n > base)
      cp.insert(insertVal + n);
    else
      cn.insert(insertVal + n);
    S -= abs(insertVal - (i));
    S += abs(insertVal - (i) + n);
    if (minS > S) {
      minS = S;
      minK = i;
    }
  }
  cout << minS << ' ' << minK;
  return 0;
}

```