#include <bits/stdc++.h>
using namespace std;
namespace Debug {
template <typename Ty>
inline void _debug(const char* f, Ty t) {
  cerr << f << '=' << t << endl;
}
template <typename Ty, typename... Ar>
inline void _debug(const char* f, Ty x, Ar... y) {
  while (*f != ',') cerr << *f++;
  cerr << '=' << x << ",";
  _debug(f + 1, y...);
}
template <typename Ty>
ostream& operator<<(ostream& os, const vector<Ty>& V) {
  os << "[";
  for (const auto& vv : V) os << vv << ",";
  os << "]";
  return os;
}
}  // namespace Debug
using namespace Debug;
namespace FastIO {
template <typename Ty>
inline void read(Ty& x) {
  char c;
  int f = 1;
  x = 0;
  while (!isdigit(c = getchar())) f = c ^ '-' ? 1 : -1;
  while (x = (x << 3) + (x << 1) + (c & 15), isdigit(c = getchar()))
    ;
  x *= f;
}
template <typename Ty, typename... Ar>
inline void read(Ty& x, Ar&... y) {
  read(x), read(y...);
}
template <typename Ty>
inline void write(Ty x) {
  x < 0 && (putchar(('-')), x = -x, 0),
      x < 10 ? (putchar((x + '0')), 0)
             : (write(x / 10), putchar((x % 10 + '0')), 0);
}
template <typename Ty>
inline void writeln(const Ty& x) {
  write(x), putchar(('\n'));
}
}  // namespace FastIO
using namespace FastIO;
const int N = 1e6 + 10;
int n, k, a[N], cnt[N << 1], c0, c1;
long long s0, s1, Ans;
int main() {
  register int i;
  for (read(n), i = 1; i <= n; i++)
    read(a[i]), a[i] > i ? ++cnt[a[i] - i], ++c0,
        s0 += a[i] - i : (++c1, s1 += i - a[i]);
  Ans = s0 + s1;
  for (i = 1; i <= n; i++)
    s0 -= c0, s1 += c1, c0 -= cnt[i], c1 += cnt[i],
        (--c1, s1 -= (n + 1) - a[n - i + 1]),
        a[n - i + 1] > 1       ? ++cnt[a[n - i + 1] - 1 + i], ++c0,
        s0 += a[n - i + 1] - 1 : ++c1, s0 + s1 < Ans && (Ans = s0 + s1, k = i);
  return write(Ans), putchar((' ')), writeln(k), 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;
namespace Debug {
template <typename Ty>
inline void _debug(const char* f, Ty t) {
  cerr << f << '=' << t << endl;
}
template <typename Ty, typename... Ar>
inline void _debug(const char* f, Ty x, Ar... y) {
  while (*f != ',') cerr << *f++;
  cerr << '=' << x << ",";
  _debug(f + 1, y...);
}
template <typename Ty>
ostream& operator<<(ostream& os, const vector<Ty>& V) {
  os << "[";
  for (const auto& vv : V) os << vv << ",";
  os << "]";
  return os;
}
}  // namespace Debug
using namespace Debug;
namespace FastIO {
template <typename Ty>
inline void read(Ty& x) {
  char c;
  int f = 1;
  x = 0;
  while (!isdigit(c = getchar())) f = c ^ '-' ? 1 : -1;
  while (x = (x << 3) + (x << 1) + (c & 15), isdigit(c = getchar()))
    ;
  x *= f;
}
template <typename Ty, typename... Ar>
inline void read(Ty& x, Ar&... y) {
  read(x), read(y...);
}
template <typename Ty>
inline void write(Ty x) {
  x < 0 && (putchar(('-')), x = -x, 0),
      x < 10 ? (putchar((x + '0')), 0)
             : (write(x / 10), putchar((x % 10 + '0')), 0);
}
template <typename Ty>
inline void writeln(const Ty& x) {
  write(x), putchar(('\n'));
}
}  // namespace FastIO
using namespace FastIO;
const int N = 1e6 + 10;
int n, k, a[N], cnt[N << 1], c0, c1;
long long s0, s1, Ans;
int main() {
  register int i;
  for (read(n), i = 1; i <= n; i++)
    read(a[i]), a[i] > i ? ++cnt[a[i] - i], ++c0,
        s0 += a[i] - i : (++c1, s1 += i - a[i]);
  Ans = s0 + s1;
  for (i = 1; i <= n; i++)
    s0 -= c0, s1 += c1, c0 -= cnt[i], c1 += cnt[i],
        (--c1, s1 -= (n + 1) - a[n - i + 1]),
        a[n - i + 1] > 1       ? ++cnt[a[n - i + 1] - 1 + i], ++c0,
        s0 += a[n - i + 1] - 1 : ++c1, s0 + s1 < Ans && (Ans = s0 + s1, k = i);
  return write(Ans), putchar((' ')), writeln(k), 0;
}

```