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#9063. Champernowne 验证

تم استخدام هذه المسألة في المسابقات التالية:

تم إعداد هذه المسألة بواسطة xiaowuc1 .

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

第 $k$ 个 Champernowne 数是通过将前 $k$ 个正整数依次连接在一起得到的。例如，第 $10$ 个 Champernowne 数是 $12345678910$。

给定一个正整数 $n$，判断它是否为一个 Champernowne 数，如果是，求出它是第几个。

输入格式

第一行包含一个整数 $n$ ($1 \le n \le 10^9$)。$n$ 不会包含前导零。

输出格式

如果 $n$ 是第 $k$ 个 Champernowne 数，输出 $k$。否则，输出 $-1$。

样例

样例输入 1

123456789

样例输出 1

样例输入 2

1000000000

样例输出 2

-1

样例输入 3

样例输出 3

-1

样例输入 4

样例输出 4

-1

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