#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007LL;
vector<vector<int> > array2_int(int N, int M, int def = 0) {
  return vector<vector<int> >(N, vector<int>(M, def));
}
vector<vector<vector<int> > > array3_int(int N, int M, int K, int def = 0) {
  return vector<vector<vector<int> > >(
      N, vector<vector<int> >(M, vector<int>(K, def)));
}
vector<vector<long long> > array2_ll(int N, int M, long long def = 0) {
  return vector<vector<long long> >(N, vector<long long>(M, def));
}
vector<vector<vector<long long> > > array3_ll(int N, int M, int K,
                                              long long def = 0) {
  return vector<vector<vector<long long> > >(
      N, vector<vector<long long> >(M, vector<long long>(K, def)));
}
template <class T>
void printImpl(const T& data) {
  cout << data << endl;
}
template <class T, int N>
void printImpl(T (&coll)[N]) {
  copy(coll, coll + N, ostream_iterator<T>(cout, " "));
  cout << endl;
}
template <class T>
void printImpl(const vector<T>& coll) {
  copy(coll.begin(), coll.end(), ostream_iterator<T>(cout, " "));
  cout << endl;
}
template <class T>
void printImpl(const vector<vector<T> >& coll) {
  for (int iii = 0; iii < coll.size(); iii++) printImpl(coll[iii]);
}
template <class Key, class Value>
void printImpl(const map<Key, Value>& data) {
  typename map<Key, Value>::const_iterator it;
  for (it = data.begin(); it != data.end(); ++it) {
    cout << it->first << ":" << it->second << endl;
  }
}
void slowSolution(const vector<int>& p) {
  int N = p.size();
  long long bestRes = 0;
  int bestShift = 0;
  for (int i = 0; i < (N); ++i) {
    bestRes += abs(p[i] - i);
  }
  for (int sh = 1; sh < N; ++sh) {
    vector<int> test(N);
    for (int i = 0; i < (N); ++i) {
      test[i] = p[(i - sh + N) % N];
    }
    long long currRes = 0;
    for (int i = 0; i < (N); ++i) {
      currRes += abs(test[i] - i);
    }
    if (currRes < bestRes) {
      bestShift = sh;
      bestRes = currRes;
    }
  }
  cout << "Slow:" << bestRes << " " << bestShift << endl;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  vector<int> p(N);
  vector<int> pos(N);
  for (int i = 0; i < (N); ++i) {
    cin >> p[i];
    p[i]--;
    pos[p[i]] = i;
  }
  vector<long long> counter(2 * N + 10);
  int negCount = 0;
  for (int i = 0; i < (N); ++i) {
    if (pos[i] < i) {
      counter[i - pos[i]]++;
      negCount++;
    }
  }
  long long curr = 0;
  for (int i = 0; i < (N); ++i) {
    curr += abs(pos[i] - i);
  }
  int bestShift = 0;
  long long bestRes = curr;
  int currShift = 0;
  for (int i = 0; i < (N - 1); ++i) {
    long long nextCurr = curr;
    int posCount = N - negCount;
    nextCurr = nextCurr - negCount + posCount;
    int currLast = p[N - 1 - i];
    int currX = N - 1 - currLast;
    nextCurr -= (2 * currX + 2 - N);
    if (currLast > 0) {
      counter[currLast + currShift + 1]++;
      negCount++;
    }
    curr = nextCurr;
    negCount -= counter[++currShift];
    if (curr < bestRes) {
      bestShift = currShift;
      bestRes = curr;
    }
  }
  cout << bestRes << " " << bestShift << endl;
  return 0;
}

### Prompt

Please create a solution in CPP to 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;
const long long MOD = 1000000007LL;
vector<vector<int> > array2_int(int N, int M, int def = 0) {
  return vector<vector<int> >(N, vector<int>(M, def));
}
vector<vector<vector<int> > > array3_int(int N, int M, int K, int def = 0) {
  return vector<vector<vector<int> > >(
      N, vector<vector<int> >(M, vector<int>(K, def)));
}
vector<vector<long long> > array2_ll(int N, int M, long long def = 0) {
  return vector<vector<long long> >(N, vector<long long>(M, def));
}
vector<vector<vector<long long> > > array3_ll(int N, int M, int K,
                                              long long def = 0) {
  return vector<vector<vector<long long> > >(
      N, vector<vector<long long> >(M, vector<long long>(K, def)));
}
template <class T>
void printImpl(const T& data) {
  cout << data << endl;
}
template <class T, int N>
void printImpl(T (&coll)[N]) {
  copy(coll, coll + N, ostream_iterator<T>(cout, " "));
  cout << endl;
}
template <class T>
void printImpl(const vector<T>& coll) {
  copy(coll.begin(), coll.end(), ostream_iterator<T>(cout, " "));
  cout << endl;
}
template <class T>
void printImpl(const vector<vector<T> >& coll) {
  for (int iii = 0; iii < coll.size(); iii++) printImpl(coll[iii]);
}
template <class Key, class Value>
void printImpl(const map<Key, Value>& data) {
  typename map<Key, Value>::const_iterator it;
  for (it = data.begin(); it != data.end(); ++it) {
    cout << it->first << ":" << it->second << endl;
  }
}
void slowSolution(const vector<int>& p) {
  int N = p.size();
  long long bestRes = 0;
  int bestShift = 0;
  for (int i = 0; i < (N); ++i) {
    bestRes += abs(p[i] - i);
  }
  for (int sh = 1; sh < N; ++sh) {
    vector<int> test(N);
    for (int i = 0; i < (N); ++i) {
      test[i] = p[(i - sh + N) % N];
    }
    long long currRes = 0;
    for (int i = 0; i < (N); ++i) {
      currRes += abs(test[i] - i);
    }
    if (currRes < bestRes) {
      bestShift = sh;
      bestRes = currRes;
    }
  }
  cout << "Slow:" << bestRes << " " << bestShift << endl;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  vector<int> p(N);
  vector<int> pos(N);
  for (int i = 0; i < (N); ++i) {
    cin >> p[i];
    p[i]--;
    pos[p[i]] = i;
  }
  vector<long long> counter(2 * N + 10);
  int negCount = 0;
  for (int i = 0; i < (N); ++i) {
    if (pos[i] < i) {
      counter[i - pos[i]]++;
      negCount++;
    }
  }
  long long curr = 0;
  for (int i = 0; i < (N); ++i) {
    curr += abs(pos[i] - i);
  }
  int bestShift = 0;
  long long bestRes = curr;
  int currShift = 0;
  for (int i = 0; i < (N - 1); ++i) {
    long long nextCurr = curr;
    int posCount = N - negCount;
    nextCurr = nextCurr - negCount + posCount;
    int currLast = p[N - 1 - i];
    int currX = N - 1 - currLast;
    nextCurr -= (2 * currX + 2 - N);
    if (currLast > 0) {
      counter[currLast + currShift + 1]++;
      negCount++;
    }
    curr = nextCurr;
    negCount -= counter[++currShift];
    if (curr < bestRes) {
      bestShift = currShift;
      bestRes = curr;
    }
  }
  cout << bestRes << " " << bestShift << endl;
  return 0;
}

```