• # For Solution

You are given a 11 by nn pixel image. The ii-th pixel of the image has color aiai. For each color, the number of pixels of that color is at most 2020.

You can perform the following operation, which works like the bucket tool in paint programs, on this image:

• pick a color — an integer from 11 to nn;
• choose a pixel in the image;
• for all pixels connected to the selected pixel, change their colors to the selected color (two pixels of the same color are considered connected if all the pixels between them have the same color as those two pixels).

Compute the minimum number of operations needed to make all the pixels in the image have the same color.

Paint solution codeforces

Each test contains multiple test cases. The first line contains the number of test cases tt (1t1031≤t≤103).

The first line of each test case contains a single integer nn (1n31031≤n≤3⋅103) — the number of pixels in the image.

The second line of each test case contains nn integers a1,a2,,ana1,a2,…,an (1ain1≤ai≤n) — the colors of the pixels in the image.

Note: for each color, the number of pixels of that color is at most 2020.

It is guaranteed that the sum of nn over all test cases does not exceed 31033⋅103.

Paint solution codeforces

For each test case, print one integer: the minimum number of operations needed to make all the pixels in the image have the same color.

Example
input

Copy
3
5
1 2 3 2 1
4
1 1 2 2
5
1 2 1 4 2

output

Paint solution codeforces
2
1
3

Note

In the first example, the optimal solution is to apply the operation on the third pixel changing its color to 22 and then to apply the operation on any pixel that has color 22 changing its color and the color of all pixels connected to it to 11. The sequence of operations is then: [1,2,3,2,1][1,2,2,2,1][1,1,1,1,1][1,2,3,2,1]→[1,2,2,2,1]→[1,1,1,1,1].

In the second example, we can either change the 11s to 22s in one operation or change the 22s to 11s also in one operation.

In the third example, one possible way to make all the pixels have the same color is to apply the operation on the first, third and the fourth pixel each time changing its color to 22.