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E - Arithmetic Number

Score : $500$ points

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.

152

159

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

88

88

$X$ itself may be an arithmetic number.

8989898989

9876543210