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G. Power Substring

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given *n* positive integers *a* _{1}, *a* _{2}, ..., *a* _{ n}.

For every *a* _{ i} you need to find a positive integer *k* _{ i} such that the decimal notation of 2^{ k i} contains the decimal notation of *a* _{ i} as a substring among its last *min*(100, *length*(2^{ k i})) digits. Here *length*(*m*) is the length of the decimal notation of *m*.

Note that you don't have to minimize *k* _{ i}. The decimal notations in this problem do not contain leading zeros.

Input

The first line contains a single integer *n* (1 ≤ *n* ≤ 2 000) — the number of integers *a* _{ i}.

Each of the next *n* lines contains a positive integer *a* _{ i} (1 ≤ *a* _{ i} < 10^{11}).

Output

Print *n* lines. The *i*-th of them should contain a positive integer *k* _{ i} such that the last *min*(100, *length*(2^{ k i})) digits of 2^{ k i} contain the decimal notation of *a* _{ i} as a substring. Integers *k* _{ i} must satisfy 1 ≤ *k* _{ i} ≤ 10^{50}.

It can be shown that the answer always exists under the given constraints. If there are multiple answers, print any of them.

Examples

Input

2

8

2

Output

3

1

Input

2

3

4857

Output

5

20

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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