There are $N$ blanks arranged in a row. The blanks are numbered $ 1, 2, \ldots , N $ from left to right.
Tom is filling each blank with one number in $\{0, 1, 2, 3\}$. According to his thought, the following $M$ conditions must all be satisfied. The $i_{th}$ condition is:
There are exactly $x_i$ different numbers among blanks $\in [l_i,r_i]$.
In how many ways can the blanks be filled to satisfy all the conditions? Find the answer modulo $998244353$.

The first line of the input contains an integer $T(1\le T \le 15)$, denoting the number of test cases.
In each test case, there are two integers $n(1 \le n \le 100)$ and $m(0 \le m \le 100)$ in the first line, denoting the number of blanks and the number of conditions.
For the following $m$ lines, each line contains three integers $l, r$ and $x$, denoting a condition$(1 \le l \le r \le n$, $1 \le x \le 4)$.

For each testcase, output a single line containing an integer, denoting the number of ways to paint the blanks satisfying all the conditions modulo $998244353$.