Generate three integers a, b, and c in [1,n] with equal probability independently, and use them as the three right-angle side length of a right-angled tetrahedron. Find the expectation of the reciprocal square of the distance from the right-angle apex to the slope (Euclidean distance).
For each test case, output a line containing the answer mod 998244353.
Input In the first line, you should read an integer T denoting the number of test cases.
In every test case, the only line will include an integer n.
It is guaranteed that T is no larger than 2×106 and n is no larger than 6×106.
Output For each test case, output the only line containing just one integer denoting the answer mod 998244353.
ll quick_pow(ll a, ll b) { ll ans = 1, base = a; while(b != 0) { if(b & 1) { ans = ans * base % mod; } base = base * base % mod; b >>= 1; } return ans; }