Ridbit 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 $1$.


-----Examples-----

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

$1$

$2 \xrightarrow{} 1$

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

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

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

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