<p>Given a positive integer <code>n</code>, return <em>the <strong>punishment number</strong></em> of <code>n</code>.</p>

<p>The <strong>punishment number</strong> of <code>n</code> is defined as the sum of the squares of all integers <code>i</code> such that:</p>

<ul>
	<li><code>1 &lt;= i &lt;= n</code></li>
	<li>The decimal representation of <code>i * i</code> can be partitioned into contiguous substrings such that the sum of the integer values of these substrings equals <code>i</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 182
<strong>Explanation:</strong> There are exactly 3 integers i that satisfy the conditions in the statement:
- 1 since 1 * 1 = 1
- 9 since 9 * 9 = 81 and 81 can be partitioned into 8 + 1.
- 10 since 10 * 10 = 100 and 100 can be partitioned into 10 + 0.
Hence, the punishment number of 10 is 1 + 81 + 100 = 182
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 37
<strong>Output:</strong> 1478
<strong>Explanation:</strong> There are exactly 4 integers i that satisfy the conditions in the statement:
- 1 since 1 * 1 = 1. 
- 9 since 9 * 9 = 81 and 81 can be partitioned into 8 + 1. 
- 10 since 10 * 10 = 100 and 100 can be partitioned into 10 + 0. 
- 36 since 36 * 36 = 1296 and 1296 can be partitioned into 1 + 29 + 6.
Hence, the punishment number of 37 is 1 + 81 + 100 + 1296 = 1478
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>

class Solution:
    def punishmentNumber(self, n: int) -> int:
        def can_partition(num_str, target, current_sum=0, index=0):
    # Base case: If we've gone through all digits
            if index == len(num_str):
                return current_sum == target
            
            # Try all possible partitions starting from index
            for end in range(index + 1, len(num_str) + 1):
                # Convert the substring into an integer
                part = int(num_str[index:end])
                
                # Check if adding this partition helps reach the target
                if can_partition(num_str, target, current_sum + part, end):
                    return True
            
            return False
        
        total_punishment = 0
    
    # Iterate over each i from 1 to n
        for i in range(1, n + 1):
            square_str = str(i * i)
            
            # Check if the square of i can be partitioned
            if can_partition(square_str, i):
                total_punishment += i * i
        
        return total_punishment
16600