G1. Light Bulbs (Easy Version)time limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThe easy and hard versions of this problem differ only in the constraints on n. In the easy version, the sum of values of n^2 over all test cases does not exceed 10^6. Furthermore, n does not exceed 1000 in each test case.There are 2n light bulbs arranged in a row. Each light bulb has a color from 1 to n (exactly two light bulbs for each color).Initially, all light bulbs are turned off. You choose a set of light bulbs S that you initially turn on. After that, you can perform the following operations in any order any number of times:  choose two light bulbs i and j of the same color, exactly one of which is on, and turn on the second one;  choose three light bulbs i, j, k, such that both light bulbs i and k are on and have the same color, and the light bulb j is between them (i < j < k), and turn on the light bulb j. You want to choose a set of light bulbs S that you initially turn on in such a way that by performing the described operations, you can ensure that all light bulbs are turned on.Calculate two numbers:  the minimum size of the set S that you initially turn on;  the number of sets S of minimum size (taken modulo 998244353). InputThe first line of the input contains a single integer t (1 \le t \le 10^4) — the number of test cases. Then follow the descriptions of the test cases.The first line of each test case contains a single integer n (2 \le n \le 1000) — the number of pairs of light bulbs.The second line of each test case contains 2n integers c_1, c_2, \dots, c_{2n} (1 \le c_i \le n), where c_i is the color of the i-th light bulb. For each color from 1 to n, exactly two light bulbs have this color.Additional constraint on the input: the sum of values of n^2 over all test cases does not exceed 10^6.OutputFor each test case, output two integers:  the minimum size of the set S that you initially turn on;  the number of sets S of minimum size (taken modulo 998244353). ExampleInput
422 2 1 121 2 2 121 2 1 253 4 4 5 3 1 1 5 2 2Output
2 4
1 2
1 4
2 8

422 2 1 121 2 2 121 2 1 253 4 4 5 3 1 1 5 2 2
2 4 1 2 1 4 2 8 
['brute force', 'combinatorics', 'dfs and similar', 'dp', 'dsu', 'graphs', 'math', 'trees', '*2100']