#SL2310D. Do You Like Interactive Problems?

Do You Like Interactive Problems?

Do You Like Interactive Problems?

There is an integer xx satisfying 1≤x≤n1 \leq x \leq n. You know nn but you don't know xx.

You can do the following guessing: pick an random integer yy uniformly satisfying 1≤y≤n1 \leq y \leq n (your yy may equal to previous queries), and you will be told if x<y,x>yorx=yx < y, x > y or x = y. You will stop asking if there is only one possible xx satisfying all the conditions.

Given nn, if xx is picked randomly uniformly, what's your expected number of queries?

Input

The first line contains an integer T (1≤T≤100)T \: (1 \leq T \leq 100) denothing the number of test cases.

For each test case, the only line contains an integer n (1≤n≤109)n \: (1 \leq n \leq 10^9).

Output

For each test case, output one integer denoting the expected number of queries modulo 998244353998244353.

Formally, it can be proven that the sought expected value can be represented as an irreducible fraction p/qp/q which satisfies q≢0 mod 998244353q \not \equiv 0 \bmod 998244353, and there is a unique integer rr satisfies 0≤r<9982443530 \leq r < 998244353 and qr≡pmod  998244353qr \equiv p \mod 998244353. Find this rr.

Example

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