Practice Mathematics with the exercise "Factorial vs Exponential"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Mathematics

Statement

Goal

For each of the given numbers A, find the smallest integer N, such that A^N < N! , where N! = 1 * 2 * ... * N
The numbers given can have up to 2 digits after decimal point.

Input

Line 1: An integer K for the number of inputs.
Line 2: K space separated numbers (can have a fractional part, e.g. 1.5): A_1, A_2, ... , A_K

Output

Line 1: K space separated integers: N_1, N_2, ... , N_K.

Constraints

1 ≤ K ≤ 100
1 < A_i < 10000

Example

Input

2
2 3

Output

4 7

Solve it

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