B'There are n uniform random real variables between 0 and 1, inclusive, which are denoted as x_1, x_2, ldots, x_n . Tenzing has m conditions. Each condition has the form of x_i+x_j <= 1 or x_i+x_j ge 1 . Tenzing wants to know the probability that all the conditions are satisfied, modulo 998~244~353 . Formally, let M = 998~244~353 . It can be shown that the answer can be expressed as an irreducible fraction frac{p}{q} , where p and q are integers and q not equiv 0 pmod{M} . Output the integer equal to p cdot q^{-1} bmod M . In other words, output the integer x that 0 <= x < M and x cdot q equiv p pmod{M} . The first line contains two integers n and m ( 1 <= n <= 20 , 0 <= m <= n^2+n ). Then following m lines of input contains three integers t , i and j ( t in {0,1 } , 1 <= i <= j <= n ). It is guaranteed that all conditions are pairwise distinct. Output the probability that all the conditions are satisfied, modulo M = 998~244~353 . In the first test case, the conditions are x_1+x_2 <= 1 and x_3+x_3 ge 1 , and the probability that each condition is satisfied is frac 12 , so the probability that they are both satisfied is frac 12 cdot frac 12= frac 14 , modulo 998~244~353 is equal to 748683265 . In the second test case, the answer is frac 14 . In the third test case, the answer is frac 1{16} . In the fourth test case, the sum of all variables must equal 2 , so the probability is 0 . '...