Magic machine#4850

Magic machine

1 second

128 megabytes

Very easy

Ibrahim has a black magic machine with three buttons and a display. The display can show at most a four-digit number. Each button changes the displayed number in some way: the first button multiplies the number by $3$ , the second adds to it the sum of its digits, and the third button subtracts $2$ . If the number becomes negative or exceeds $9999$ , the machine breaks.

Ibrahim can press the buttons in any order. He wonders how to display the number $b$ after some sequence of button presses, starting from the number $a$ currently shown on the display. Help him find the minimum number of button presses required.

Input

Two integers $a$ and $b$ ( $1 \leq a, b \leq 9999$ 1 \leq a, b \leq 9999) are given.

Output

Print the minimum number of operations needed to obtain $b$ from $a$ .

Examples

Example 1

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Example 2

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Example 3

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1 \leq a, b \leq 9999