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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.

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