| # 820_D. Mister B and PR Shifts |
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| ## Problem Description |
| Some time ago Mister B detected a strange signal from the space, which he started to study. |
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| 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. |
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| Let's define the deviation of a permutation p as <image>. |
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| Find a cyclic shift of permutation p with minimum possible deviation. If there are multiple solutions, print any of them. |
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| 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: |
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| * k = 0: shift p1, p2, ... pn, |
| * k = 1: shift pn, p1, ... pn - 1, |
| * ..., |
| * k = n - 1: shift p2, p3, ... pn, p1. |
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| Input |
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| First line contains single integer n (2 ≤ n ≤ 106) — the length of the permutation. |
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| 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. |
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| Output |
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| 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. |
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| Examples |
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| Input |
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| 3 |
| 1 2 3 |
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| Output |
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| 0 0 |
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| Input |
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| 3 |
| 2 3 1 |
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| Output |
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| 0 1 |
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| Input |
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| 3 |
| 3 2 1 |
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| Output |
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| 2 1 |
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| Note |
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| 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. |
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| 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. |
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| 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. |
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| ## Contest Information |
| - **Contest ID**: 820 |
| - **Problem Index**: D |
| - **Points**: 1000.0 |
| - **Rating**: 1900 |
| - **Tags**: data structures, implementation, math |
| - **Time Limit**: {'seconds': 2, 'nanos': 0} seconds |
| - **Memory Limit**: 256000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
