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.
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline bool chkmin(T &a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T>
inline bool chkmax(T &a, T b) {
  return a < b ? a = b, 1 : 0;
}
namespace IO {
const int maxin = 1000000;
const int maxout = 1000000;
char _Input[maxin + 10], *_beg, *_end;
char _Output[maxout], *_pointer = _Output;
inline void init() {
  int _ = fread(_Input, 1, maxin, stdin);
  _beg = _Input, _end = _Input + _;
}
inline void Getchar() {
  if (++_beg == _end) {
    int _ = fread(_Input, 1, maxin, stdin);
    _beg = _Input, _end = _Input + _;
  }
}
template <typename Type>
inline Type read() {
  Type x = 0, f = 1;
  while (!isdigit(*_beg)) {
    if (*_beg == '-') f = -1;
    Getchar();
  }
  while (isdigit(*_beg)) {
    x = x * 10 + *_beg - '0';
    Getchar();
  }
  return x * f;
}
template <typename Type>
inline void Write(Type x, char ln = '\n') {
  static Type owo[54], qwq = 0;
  if (x < 0) x = -x, *_pointer++ = '-';
  do owo[++qwq] = x % 10;
  while (x /= 10);
  while (qwq) *_pointer++ = '0' + owo[qwq--];
  *_pointer++ = ln;
}
inline int gets(char *s) {
  char *t = s;
  while (!isalpha(*_beg))
    ;
  do *s++ = *_beg;
  while (Getchar(), isalpha(*_beg));
  *s = 0;
  return s - t;
}
inline void puts(char *s, char ln = '\n') {
  while (*s) *_pointer++ = *s++;
  *_pointer++ = ln;
}
inline void output() {
  fwrite(_Output, _pointer - _Output, 1, stdout);
  _pointer = _Output;
}
}  // namespace IO
const int maxn = 1000000 + 10;
int n;
int delta;
long long sum;
int a[maxn];
int bot[maxn];
inline void init() {
  n = IO::read<int>();
  for (int i = 1; i <= n; a[i++] = IO::read<int>())
    ;
  for (int i = 1; i <= n; i++)
    if (a[i] >= i) {
      delta--;
      sum += a[i] - i;
      bot[a[i] - i]++;
    } else {
      delta++;
      sum += i - a[i];
      bot[n - i + a[i]]++;
    }
}
inline void exec() {
  int pos = 0;
  long long ans = sum;
  for (int i = 1; i < n; i++) {
    delta += bot[i - 1] << 1;
    delta -= 2;
    sum += abs(a[n - i + 1] - 1) - abs(a[n - i + 1] - n) + delta + 1;
    if (chkmin(ans, sum)) pos = i;
  }
  IO::Write(ans, ' ');
  IO::Write(pos);
}
int main() {
  if (fopen("819B.in", "r") != NULL) {
    freopen("819B.in", "r", stdin);
    freopen("819B.out", "w", stdout);
  }
  IO::init();
  init();
  exec();
  IO::output();
  return 0;
}
