A8081 | Reflection

For 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 contains two space-separated integers $l$ and $r$ ( $1<=l<=r<=10^{9}$ ) — bounds of the range.

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).