Avoid Local Maximums

2000ms

262144K

Description:

You are given an array $$$a$$$ of size $$$n$$$. Each element in this array is an integer between $$$1$$$ and $$$10^9$$$.

You can perform several operations to this array. During an operation, you can replace an element in the array with any integer between $$$1$$$ and $$$10^9$$$.

Output the minimum number of operations needed such that the resulting array doesn't contain any local maximums, and the resulting array after the operations.

An element $$$a_i$$$ is a local maximum if it is strictly larger than both of its neighbors (that is, $$$a_i > a_{i - 1}$$$ and $$$a_i > a_{i + 1}$$$). Since $$$a_1$$$ and $$$a_n$$$ have only one neighbor each, they will never be a local maximum.

Input:

Each test contains multiple test cases. The first line will contain a single integer $$$t$$$ $$$(1 \leq t \leq 10000)$$$ — the number of test cases. Then $$$t$$$ test cases follow.

The first line of each test case contains a single integer $$$n$$$ $$$(2 \leq n \leq 2 \cdot 10^5)$$$ — the size of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots ,a_n$$$ $$$(1 \leq a_i \leq 10^9)$$$, the elements of array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, first output a line containing a single integer $$$m$$$ — minimum number of operations required. Then ouput a line consist of $$$n$$$ integers — the resulting array after the operations. Note that this array should differ in exactly $$$m$$$ elements from the initial array.

If there are multiple answers, print any.

Sample Input:

5
3
2 1 2
4
1 2 3 1
5
1 2 1 2 1
9
1 2 1 3 2 3 1 2 1
9
2 1 3 1 3 1 3 1 3

Sample Output:

0
2 1 2
1
1 3 3 1
1
1 2 2 2 1
2
1 2 3 3 2 3 3 2 1
2
2 1 3 3 3 1 1 1 3

Note:

In the first example, the array contains no local maximum, so we don't need to perform operations.

In the second example, we can change $$$a_2$$$ to $$$3$$$, then the array don't have local maximums.

Informação

Provedor Codeforces

Código CF1635B