You have just learned the algorithm bubble sort , which is able to sort an array in non-descending order. Let's define the function (\text{sort}(a)) as in the following pseudocode: As it is shown, the return value of (\text{sort}(a)) represents the number of rounds needed to make array (a) sorted in non-descending order by using bubble sort . You are given an integer (n), as well as (m) integer tuples ((k_i,l_i,r_i)) ((1\le i\le m)). Count the number of permutations(^{\text{∗}}) (p) of length (n), modulo (998\,244\,353), so that the following restrictions are satisfied: For each (1\le i\le n), let (b_i=\text{sort}(p_1,p_2,\ldots,p_{i})), then For each (1\le j\le m), let (x) be the number of indices (y) ((1\le y\le n)) such that (b_y\le k_j), then (l_j\le x\le r_j) holds. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains two integers (n) and (m) ((2\leq n\leq 10^6), (0\leq m\leq 1000)). Then (m) lines follow, the (i)-th line containing three integers (k_i), (l_i), and (r_i) ((0\le k_i\le n - 1), (1\le l_i\le r_i\le n)) — the restrictions. It is guaranteed that the sum of (m^2) over all test cases does not exceed (10^6). For each test case, output a single integer — the number of possible permutations, modulo (998\,244\,353). In the first test case, only permutations (3,1,4,2) and (4,1,3,2) satisfy the re