Find the Punishment Number

Description

Given a positive integer ( n ), return its punishment number.

The punishment number of ( n ) is the sum of squares of all numbers ( i ) (where ( $1 \leq i \leq n$ )) that satisfy:

• ( $i^2$ ) can be split into contiguous substrings,
• The sum of these substrings equals ( i ).

Example 1

Input:

n = 12

Output:

182

Explanation: Numbers satisfying the condition:

• ( $1^2 = 1$) ✅
• ($9^2 = 81 \rightarrow 8 + 1 = 9$) ✅
• ( $10^2 = 100 \rightarrow 10 + 0 = 10$) ✅

Total punishment number: ( 1 + 81 + 100 = 182 )

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Example 2

Input:

n = 25

Output:

182

Explanation: Numbers satisfying the condition:

• ($1^2 = 1$ ) ✅
• ($9^2 = 81 \rightarrow 8 + 1 = 9$) ✅
• ($10^2 = 100 \rightarrow 10 + 0 = 10$ ) ✅

Total punishment number: ( 1 + 81 + 100 = 182 )

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Constraints

$1 \leq n \leq 1000$