#include <bits/stdc++.h>
using namespace std;
struct seg {
  long long int leftmost, rightmost;
} lazy_tree[7000005];
int p[1000005];
int curShift, shiftAns;
long long int ans;
void build_segment_tree(int node, int a, int b) {
  if (b < a) {
    return;
  }
  if (a == b) {
    lazy_tree[node].leftmost = 0;
    lazy_tree[node].rightmost = 0;
    return;
  }
  lazy_tree[node].leftmost = lazy_tree[node].rightmost = 0;
  build_segment_tree(2 * node, a, (a + b) / 2);
  build_segment_tree(2 * node, (a + b) / 2 + 1, b);
  return;
}
void update_segment_tree(int node, int a, int b, int l, int r,
                         long long int valLeft, long long int valRight) {
  long long int range, leftRange, rightRange, totalNode;
  if (b < a) {
    return;
  }
  if (b < l || a > r) {
    return;
  }
  if (a == l && b == r) {
    lazy_tree[node].leftmost += valLeft;
    lazy_tree[node].rightmost += valRight;
    return;
  }
  if (r <= (a + b) / 2) {
    update_segment_tree(2 * node, a, (a + b) / 2, l, r, valLeft, valRight);
  } else if ((a + b) / 2 < l) {
    update_segment_tree(2 * node + 1, (a + b) / 2 + 1, b, l, r, valLeft,
                        valRight);
  } else {
    range = r - l + (long long int)1;
    leftRange = (a + b) / 2 - l + (long long int)1;
    rightRange = range - leftRange;
    if (valLeft <= valRight) {
      totalNode = valRight - valLeft + (long long int)1;
      update_segment_tree(
          2 * node, a, (a + b) / 2, l, (a + b) / 2, valLeft,
          valLeft - (long long int)1 + (leftRange * totalNode) / range);
      update_segment_tree(
          2 * node + 1, (a + b) / 2 + 1, b, (a + b) / 2 + 1, r,
          valRight + (long long int)1 - (rightRange * totalNode) / range,
          valRight);
    } else {
      totalNode = -valRight + valLeft + (long long int)1;
      update_segment_tree(
          2 * node, a, (a + b) / 2, l, (a + b) / 2, valLeft,
          valLeft + (long long int)1 - (leftRange * totalNode) / range);
      update_segment_tree(
          2 * node + 1, (a + b) / 2 + 1, b, (a + b) / 2 + 1, r,
          valRight - (long long int)1 + (rightRange * totalNode) / range,
          valRight);
    }
  }
  return;
}
void query_segment_tree(int node, int a, int b) {
  long long int range, leftRange, rightRange, totalNode, leftNode, rightNode;
  long long int ansLeft = -1, ansRight = -1, diff;
  if (b < a) {
    return;
  }
  if (a != b) {
    totalNode = b - a + (long long int)1;
    leftNode = (a + b) / 2 - a + (long long int)1;
    rightNode = totalNode - leftNode;
    diff = (lazy_tree[node].rightmost - lazy_tree[node].leftmost) / (b - a);
    lazy_tree[2 * node].leftmost += lazy_tree[node].leftmost;
    lazy_tree[2 * node].rightmost +=
        lazy_tree[node].leftmost + ((b + a) / 2 - a) * diff;
    lazy_tree[2 * node + 1].leftmost +=
        lazy_tree[node].leftmost + ((a + b) / 2 - a + (long long int)1) * diff;
    lazy_tree[2 * node + 1].rightmost += lazy_tree[node].rightmost;
  }
  if (a == b) {
    curShift++;
    if (ans == -1) {
      shiftAns = curShift;
      ans = lazy_tree[node].leftmost;
    } else {
      if (ans > lazy_tree[node].leftmost) {
        ans = lazy_tree[node].leftmost;
        shiftAns = curShift;
      }
    }
    return;
  }
  query_segment_tree(2 * node, a, (a + b) / 2);
  query_segment_tree(2 * node + 1, (a + b) / 2 + 1, b);
  return;
}
void debug() {
  for (int i = 1; i <= 19; i++) {
    cout << "node";
    cout << i << "range " << lazy_tree[i].leftmost << " "
         << lazy_tree[i].rightmost << endl;
  }
}
int main() {
  int n, i, lastIdx;
  cin >> n;
  for (i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
  }
  build_segment_tree(1, 0, n - 1);
  for (i = 1; i <= n; i++) {
    if (p[i] >= i) {
      lastIdx = p[i] - i;
      update_segment_tree(1, 0, n - 1, 0, p[i] - i, p[i] - i, 0);
      if (p[i] < n) {
        lastIdx = n - i;
        update_segment_tree(1, 0, n - 1, p[i] - i + 1, n - i, 1, n - p[i]);
      }
      if (i > 1) {
        update_segment_tree(1, 0, n - 1, lastIdx + 1, n - 1, p[i] - 1,
                            p[i] - (i - 1));
      }
    } else if (p[i] < i) {
      update_segment_tree(1, 0, n - 1, 0, n - i, i - p[i], n - p[i]);
      update_segment_tree(1, 0, n - 1, n - i + 1, n - i + p[i], p[i] - 1, 0);
      if (i - p[i] > 1) {
        update_segment_tree(1, 0, n - 1, n - i + 1 + p[i], n - 1, 1,
                            i - 1 - p[i]);
      }
    }
  }
  ans = curShift = shiftAns = -1;
  query_segment_tree(1, 0, n - 1);
  cout << ans << " " << shiftAns;
  return 0;
}

### 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;
struct seg {
  long long int leftmost, rightmost;
} lazy_tree[7000005];
int p[1000005];
int curShift, shiftAns;
long long int ans;
void build_segment_tree(int node, int a, int b) {
  if (b < a) {
    return;
  }
  if (a == b) {
    lazy_tree[node].leftmost = 0;
    lazy_tree[node].rightmost = 0;
    return;
  }
  lazy_tree[node].leftmost = lazy_tree[node].rightmost = 0;
  build_segment_tree(2 * node, a, (a + b) / 2);
  build_segment_tree(2 * node, (a + b) / 2 + 1, b);
  return;
}
void update_segment_tree(int node, int a, int b, int l, int r,
                         long long int valLeft, long long int valRight) {
  long long int range, leftRange, rightRange, totalNode;
  if (b < a) {
    return;
  }
  if (b < l || a > r) {
    return;
  }
  if (a == l && b == r) {
    lazy_tree[node].leftmost += valLeft;
    lazy_tree[node].rightmost += valRight;
    return;
  }
  if (r <= (a + b) / 2) {
    update_segment_tree(2 * node, a, (a + b) / 2, l, r, valLeft, valRight);
  } else if ((a + b) / 2 < l) {
    update_segment_tree(2 * node + 1, (a + b) / 2 + 1, b, l, r, valLeft,
                        valRight);
  } else {
    range = r - l + (long long int)1;
    leftRange = (a + b) / 2 - l + (long long int)1;
    rightRange = range - leftRange;
    if (valLeft <= valRight) {
      totalNode = valRight - valLeft + (long long int)1;
      update_segment_tree(
          2 * node, a, (a + b) / 2, l, (a + b) / 2, valLeft,
          valLeft - (long long int)1 + (leftRange * totalNode) / range);
      update_segment_tree(
          2 * node + 1, (a + b) / 2 + 1, b, (a + b) / 2 + 1, r,
          valRight + (long long int)1 - (rightRange * totalNode) / range,
          valRight);
    } else {
      totalNode = -valRight + valLeft + (long long int)1;
      update_segment_tree(
          2 * node, a, (a + b) / 2, l, (a + b) / 2, valLeft,
          valLeft + (long long int)1 - (leftRange * totalNode) / range);
      update_segment_tree(
          2 * node + 1, (a + b) / 2 + 1, b, (a + b) / 2 + 1, r,
          valRight - (long long int)1 + (rightRange * totalNode) / range,
          valRight);
    }
  }
  return;
}
void query_segment_tree(int node, int a, int b) {
  long long int range, leftRange, rightRange, totalNode, leftNode, rightNode;
  long long int ansLeft = -1, ansRight = -1, diff;
  if (b < a) {
    return;
  }
  if (a != b) {
    totalNode = b - a + (long long int)1;
    leftNode = (a + b) / 2 - a + (long long int)1;
    rightNode = totalNode - leftNode;
    diff = (lazy_tree[node].rightmost - lazy_tree[node].leftmost) / (b - a);
    lazy_tree[2 * node].leftmost += lazy_tree[node].leftmost;
    lazy_tree[2 * node].rightmost +=
        lazy_tree[node].leftmost + ((b + a) / 2 - a) * diff;
    lazy_tree[2 * node + 1].leftmost +=
        lazy_tree[node].leftmost + ((a + b) / 2 - a + (long long int)1) * diff;
    lazy_tree[2 * node + 1].rightmost += lazy_tree[node].rightmost;
  }
  if (a == b) {
    curShift++;
    if (ans == -1) {
      shiftAns = curShift;
      ans = lazy_tree[node].leftmost;
    } else {
      if (ans > lazy_tree[node].leftmost) {
        ans = lazy_tree[node].leftmost;
        shiftAns = curShift;
      }
    }
    return;
  }
  query_segment_tree(2 * node, a, (a + b) / 2);
  query_segment_tree(2 * node + 1, (a + b) / 2 + 1, b);
  return;
}
void debug() {
  for (int i = 1; i <= 19; i++) {
    cout << "node";
    cout << i << "range " << lazy_tree[i].leftmost << " "
         << lazy_tree[i].rightmost << endl;
  }
}
int main() {
  int n, i, lastIdx;
  cin >> n;
  for (i = 1; i <= n; i++) {
    scanf("%d", &p[i]);
  }
  build_segment_tree(1, 0, n - 1);
  for (i = 1; i <= n; i++) {
    if (p[i] >= i) {
      lastIdx = p[i] - i;
      update_segment_tree(1, 0, n - 1, 0, p[i] - i, p[i] - i, 0);
      if (p[i] < n) {
        lastIdx = n - i;
        update_segment_tree(1, 0, n - 1, p[i] - i + 1, n - i, 1, n - p[i]);
      }
      if (i > 1) {
        update_segment_tree(1, 0, n - 1, lastIdx + 1, n - 1, p[i] - 1,
                            p[i] - (i - 1));
      }
    } else if (p[i] < i) {
      update_segment_tree(1, 0, n - 1, 0, n - i, i - p[i], n - p[i]);
      update_segment_tree(1, 0, n - 1, n - i + 1, n - i + p[i], p[i] - 1, 0);
      if (i - p[i] > 1) {
        update_segment_tree(1, 0, n - 1, n - i + 1 + p[i], n - 1, 1,
                            i - 1 - p[i]);
      }
    }
  }
  ans = curShift = shiftAns = -1;
  query_segment_tree(1, 0, n - 1);
  cout << ans << " " << shiftAns;
  return 0;
}

```