Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Reflection

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFor each positive integer *n* consider the integer ψ(*n*) which is obtained from *n* by replacing every digit *a* in the decimal notation of *n* with the digit (9 - *a*). We say that ψ(*n*) is the reflection of *n*. For example, reflection of 192 equals 807. Note that leading zeros (if any) should be omitted. So reflection of 9 equals 0, reflection of 91 equals 8.

Let us call the weight of the number the product of the number and its reflection. Thus, the weight of the number 10 is equal to 10·89 = 890.

Your task is to find the maximum weight of the numbers in the given range [*l*, *r*] (boundaries are included).

Input

Input contains two space-separated integers *l* and *r* (1 ≤ *l* ≤ *r* ≤ 10^{9}) — bounds of the range.

Output

Output should contain single integer number: maximum value of the product *n*·ψ(*n*), where *l* ≤ *n* ≤ *r*.

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preferred to use cout (also you may use %I64d).

Examples

Input

3 7

Output

20

Input

1 1

Output

8

Input

8 10

Output

890

Note

In the third sample weight of 8 equals 8·1 = 8, weight of 9 equals 9·0 = 0, weight of 10 equals 890.

Thus, maximum value of the product is equal to 890.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/27/2020 23:19:03 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|