can you give me a solution to this problem: 'A number sequence [a_1, a_2, …, a_n] is lucky if and only if the following requirements are fulfilled.

Each element a_i in the sequence is a non-negative integer such that 0 ≤ (a_i)/(i) < \frac{√{5} + 1}{2};
For any two elements a_i and a_j (i ≠ j) in the sequence, a_i ≠ 0 and a_j ≠ 0 imply that a_i ≠ a_j.
Your task is to figure out how many number sequences of length n are lucky and report the number modulo 998 244 353.

Input

The first line contains an integer T (1 ≤ T ≤ 10^5), indicating the number of test cases.

Then follow T test cases. For each test case:

The only line contains an integer n (1 ≤ n ≤ 10^5), indicating the length of the sequence.

Output

For each test case, output an integer in one line, representing the number of lucky sequences of length n modulo 998 244 353.

Example

Input

5
1
2
3
4
5

Output

2
7
27
141
919

Note

For n = 2, there are 7 lucky sequences: [0, 0], [0, 1], [0, 2], [0, 3], [1, 0], [1, 2] and [1, 3].'
in python