Find the Punishment Number of an Integer
<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 in the range [1, 10] that satisfy the conditions in the statement:
- 1 since 1 * 1 = 1
- 9 since 9 * 9 = 81 and 81 can be partitioned into 8 and 1 with a sum equal to 8 + 1 == 9.
- 10 since 10 * 10 = 100 and 100 can be partitioned into 10 and 0 with a sum equal to 10 + 0 == 10.
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 in the range [1, 37] 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>
Math; Backtracking
class Solution:
    def punishmentNumber(self, n: int) -> int:
        def check(s: str, i: int, x: int) -> bool:
            m = len(s)
            if i >= m:
                return x == 0
            y = 0
            for j in range(i, m):
                y = y * 10 + int(s[j])
                if y > x:
                    break
                if check(s, j + 1, x - y):
                    return True
            return False

        ans = 0
        for i in range(1, n + 1):
            x = i * i
            if check(str(x), 0, i):
                ans += x
        return ans
