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A. Subtract or Divide

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputRidbit starts with an integer $$$n$$$.

In one move, he can perform one of the following operations:

- divide $$$n$$$ by one of its proper divisors, or
- subtract $$$1$$$ from $$$n$$$ if $$$n$$$ is greater than $$$1$$$.

A proper divisor is a divisor of a number, excluding itself. For example, $$$1$$$, $$$2$$$, $$$4$$$, $$$5$$$, and $$$10$$$ are proper divisors of $$$20$$$, but $$$20$$$ itself is not.

What is the minimum number of moves Ridbit is required to make to reduce $$$n$$$ to $$$1$$$?

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The only line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 10^9$$$).

Output

For each test case, output the minimum number of moves required to reduce $$$n$$$ to $$$1$$$.

Example

Input

6 1 2 3 4 6 9

Output

0 1 2 2 2 3

Note

For the test cases in the example, $$$n$$$ may be reduced to $$$1$$$ using the following operations in sequence

$$$1$$$

$$$2 \xrightarrow{} 1$$$

$$$3 \xrightarrow{} 2 \xrightarrow{} 1$$$

$$$4 \xrightarrow{} 2 \xrightarrow{} 1$$$

$$$6 \xrightarrow{} 2 \xrightarrow{} 1$$$

$$$9 \xrightarrow{} 3 \xrightarrow{} 2\xrightarrow{} 1$$$

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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