MainKing has a rooted tree with nnn nodes, and mmm paths on it. And the root of this tree is 111. The endpoints of the i-th path are ai,bia_i,b_iai,bi. All of these paths satisfy a special condition:
MainKing has a rooted tree with nnn nodes, and mmm paths on it. And the root of this tree is 111. The endpoints of the i-th path are ai,bia_i,b_iai,bi. All of these paths satisfy a special condition: aia_iai is on the path from bib_ibi to the root. Now MianKing wants to delete all of these paths. He will do the following operation until all of the paths are deleted: choose an integer xxx from [1,n][1,n][1,n] randomly and delete all of the paths where xxx is on. MianKing wants you to calculate the expected number of operations he need to do. It's guaranteed that the answer will converge to some rational number. If the answer is irreducible fraction xyfrac{x}{y}yx, you need to output an integer ddd in [0,998244352][0,998244352][0,998244352] which satisfies d×y mod 998244353=x mod 998244353dtimes y~mod~998244353=x~mod~998244353d×y mod 998244353=x mod 998244353. It's guaranteed that y mod 998244353≠0y~mod~998244353neq 0y mod 998244353=0
