#include <bits/stdc++.h>
using namespace std;
inline void scf(int &x) { scanf("%d", &x); }
inline void scf(long long &x) { scanf("%I64d", &x); }
inline void scf(unsigned long long &x) { scanf("%I64u", &x); }
inline void scf(double &x) { scanf("%lf", &x); }
inline void scf(char &x) { scanf("%c", &x); }
inline void scf(char *x) { scanf("%s", x); }
const int N = 2e6 + 7;
const int mars = 0x3c3c3c3c;
typedef int Arr[N];
typedef char Err[N];
typedef bool Brr[N];
typedef long long Lrr[N];
int m, n, k, w, a, b, c, d, p, q, x, y, cnt, l;
long long t, s;
Arr A, M;
int main() {
  int i, u, v;
  scf(n);
  for (i = 1; i <= n; i++) {
    scf(A[i]), t += abs(A[i] - i);
    if (A[i] > i) M[A[i] - i]++, cnt++;
  }
  s = t;
  for (i = 1; i < n; i++) {
    x = n - i + 1;
    t += n - 2 * cnt, cnt -= M[i];
    t -= abs(A[x] - n - 1), t += abs(A[x] - 1);
    if (t < s) s = t, l = i;
    if (A[x] > x && A[x] - x > i) M[A[x] - x]--, cnt--;
    if (A[x] != 1) M[i + A[x] - 1]++, cnt++;
  }
  cout << s << ' ' << l;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
inline void scf(int &x) { scanf("%d", &x); }
inline void scf(long long &x) { scanf("%I64d", &x); }
inline void scf(unsigned long long &x) { scanf("%I64u", &x); }
inline void scf(double &x) { scanf("%lf", &x); }
inline void scf(char &x) { scanf("%c", &x); }
inline void scf(char *x) { scanf("%s", x); }
const int N = 2e6 + 7;
const int mars = 0x3c3c3c3c;
typedef int Arr[N];
typedef char Err[N];
typedef bool Brr[N];
typedef long long Lrr[N];
int m, n, k, w, a, b, c, d, p, q, x, y, cnt, l;
long long t, s;
Arr A, M;
int main() {
  int i, u, v;
  scf(n);
  for (i = 1; i <= n; i++) {
    scf(A[i]), t += abs(A[i] - i);
    if (A[i] > i) M[A[i] - i]++, cnt++;
  }
  s = t;
  for (i = 1; i < n; i++) {
    x = n - i + 1;
    t += n - 2 * cnt, cnt -= M[i];
    t -= abs(A[x] - n - 1), t += abs(A[x] - 1);
    if (t < s) s = t, l = i;
    if (A[x] > x && A[x] - x > i) M[A[x] - x]--, cnt--;
    if (A[x] != 1) M[i + A[x] - 1]++, cnt++;
  }
  cout << s << ' ' << l;
}

```