A. Reflection

Codeforces

IDCF86A

Time2000ms

Memory256MB

Difficulty—

math

English · Original

Chinese · Translation

Formal · Original

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 Input contains two space-separated integers _l_ and _r_ (1 ≤ _l_ ≤ _r_ ≤ 109) — 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_). [samples] ## 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.

对于每个正整数 $n$，考虑整数 $\psi(n)$，它通过将 $n$ 的十进制表示中的每一位数字 $a$ 替换为数字 $(9 - a)$ 得到。我们称 $\psi(n)$ 为 $n$ 的 _反射_。例如，$192$ 的反射等于 $807$。注意，前导零（如果有）应被省略。因此，$9$ 的反射等于 $0$，$91$ 的反射等于 $8$。我们称一个数的 _权重_ 为该数与其反射的乘积。因此，数 $10$ 的权重等于 $10 \cdot 89 = 890$。你的任务是找出给定范围 $[l, r]$（包含端点）内所有数的最大权重。输入包含两个用空格分隔的整数 $l$ 和 $r$（$1 \leq l \leq r \leq 10^9$）——范围的边界。输出应包含一个整数：最大乘积 $n \cdot \psi(n)$ 的值，其中 $l \leq n \leq r$。请不要在 C++ 中使用 _%lld_ 标识符读取或写入 64 位整数。建议使用 _cout_（你也可以使用 _%I64d_）。 ## Input 输入包含两个用空格分隔的整数 $l$ 和 $r$（$1 \leq l \leq r \leq 10^9$）——范围的边界。 ## Output 输出应包含一个整数：最大乘积 $n \cdot \psi(n)$ 的值，其中 $l \leq n \leq r$。请不要在 C++ 中使用 _%lld_ 标识符读取或写入 64 位整数。建议使用 _cout_（你也可以使用 _%I64d_）。 [samples] ## Note 在第三个样例中，$8$ 的权重等于 $8 \cdot 1 = 8$，$9$ 的权重等于 $9 \cdot 0 = 0$，$10$ 的权重等于 $890$。因此，乘积的最大值等于 $890$。

**Definitions** Let $\psi(n)$ denote the reflection of a positive integer $n$, obtained by replacing each digit $a$ in the decimal representation of $n$ with $9 - a$, and removing leading zeros. Let $w(n) = n \cdot \psi(n)$ denote the weight of $n$. **Constraints** Given integers $l, r \in \mathbb{Z}$ such that $1 \leq l \leq r \leq 10^9$. **Objective** Find $$ \max_{n \in [l, r]} w(n) = \max_{n \in [l, r]} \left( n \cdot \psi(n) \right) $$

Samples

Input #1

3 7

Output #1

Input #2

1 1

Output #2

Input #3

8 10

Output #3

API Response (JSON)

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