Minimum Paper Score Challenge

In this problem, the scoring strategy is modified because the exam was unusually difficult. The teacher decided to adopt a "square-root times ten" scoring system. Specifically, if the raw exam score is \( x \) points, then the score displayed on the transcript is \( \lfloor 10\sqrt{x} \rfloor \) points.

Note:

• For any non-negative number \( x \), \( \sqrt{x} \) denotes its arithmetic square root. That is, if \( y\ge0 \) and \( y \times y = x \), then \( y=\sqrt{x} \). For example, \( \sqrt{9} = 3 \).
• \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \); for instance, \( \lfloor 4.2 \rfloor = 4 \).

It is given that both the raw exam score and the transcript score are non-negative integers. In particular, Xiao Fentu's class teacher demands that his transcript score must be at least \( a \) points. Being a genius, he can score any raw exam score he wishes, and now he challenges himself to achieve at least \( a \) points with the smallest possible raw exam score.

Formally, given a non-negative integer \( a \), find the smallest non-negative integer \( x \) such that \[ \lfloor 10 \sqrt{x} \rfloor \ge a. \]

inputFormat

The input consists of a single non-negative integer \( a \) representing the minimum required transcript score.

\(\textbf{Constraints}:\)

• \( 0 \leq a \leq 10^9 \)

outputFormat

Output the smallest non-negative integer \( x \) (the raw exam score) such that \( \lfloor 10\sqrt{x} \rfloor \ge a \).

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