An integer sequence $b_1, b_2, \ldots, b_m$ is a pyramid if it satisfies the following conditions:
$m$is odd.- For each valid
$i$,$b_i = min(i, m - i + 1)$.
For example, $[1, 2, 3, 4, 3, 2, 1]$ is a pyramid, but $[1, 2, 3, 3, 2, 1]$ and $[1, 3, 2]$ are not.
An integer sequence $c_1, c_2, \ldots, c_k$ is good if it is possible to make it a pyramid by performing the following operation any number of times:
- Select an element, and decrease it by exactly
$1$. Formally, select a valid index$i$, and then, assign$c_i := c_i - 1$.
The cost of a good sequence is the minimum number of times you have to perform the above operation to make it good.
You are given an integer sequence $a_1, a_2, \ldots a_n$. You have to find the maximum length of a subarray which is good and among all such subarrays, you have to find the one with the minimum cost.
The subarray of an array $a$ with length $n$ is a contiguous part of the array, i. e. the sequence $𝑎_𝑖,𝑎_{𝑖+1},…,𝑎_𝑗$ for some $1 \le i \le j \le n$.
Input
The first line of the input contains a single integer $t(1 \le t \le 10)$ denoting the number of test cases. The description of $t$ test cases follows.
The first line of each test case contains a single integer $n(1 \le n \le 2 \cdot 10^6)$.
The second line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n( 1 \le a_i \le 2 \cdot 10^6)$.
The sum of $n$ over all test cases does not exceed $2 \cdot 10^6$.
Output
For each test case, print two space-separated integers — the maximum length of a good subarray and the minimum cost of all good subarrays with the maximum length.
Sample
| Input | Output |
|---|---|
4 5 1 1 5 2 3 4 1 4 2 1 3 1 2 1 10 1 4 4 2 3 5 6 4 2 1 | 3 4 3 3 3 0 7 7 |
