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, $$$a_i \gt a_{i - 1}$$$ and $$$a_i \gt a_{i + 1}$$$). 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.

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.

Avoid Local Maximums

Examples