Score : $500$ points

问题描述

让我们称满足以下条件的正整数 $n$ 为 等差数。

• 当 $n$ 以十进制表示且没有前导零时，令 $d_i$ 表示从高位开始的第 $i$ 个数字。则有 $(d_2-d_1)=(d_3-d_2)=\dots=(d_k-d_{k-1})$ 成立，其中 $k$ 是 $n$ 的位数。
  • 这个条件可以重述为序列 $(d_1,d_2,\dots,d_k)$ 是等差的。
  • 若 $n$ 是一位数，则假设它是等差数。

例如，$234, 369, 86420, 17, 95, 8, 11, 777$ 都是等差数，而 $751, 919, 2022, 246810, 2356$ 则不是。

找出大于等于 $X$ 的最小的等差数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Let us call a positive integer $n$ that satisfies the following condition an arithmetic number.

• Let $d_i$ be the $i$-th digit of $n$ from the top (when $n$ is written in base $10$ without unnecessary leading zeros.) Then, $(d_2-d_1)=(d_3-d_2)=\dots=(d_k-d_{k-1})$ holds, where $k$ is the number of digits in $n$.
  • This condition can be rephrased into the sequence $(d_1,d_2,\dots,d_k)$ being arithmetic.
  • If $n$ is a $1$-digit integer, it is assumed to be an arithmetic number.

For example, $234,369,86420,17,95,8,11,777$ are arithmetic numbers, while $751,919,2022,246810,2356$ are not.

Find the smallest arithmetic number not less than $X$.

Constraints

• $X$ is an integer between $1$ and $10^{17}$ (inclusive).

Input

Input is given from Standard Input in the following format:

$X$

Output

Print the answer as an integer.

Sample Input 1

152

Sample Output 1

159

The smallest arithmetic number not less than $152$ is $159$.

Sample Input 2

88

Sample Output 2

88

$X$ itself may be an arithmetic number.

Sample Input 3

8989898989

Sample Output 3

9876543210

update @ 2024/3/10 10:10:27