<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 check(self, num, square_string) -> bool:
        path = []
        n = len(square_string)
        check = []
        def dfs(i):
            if i == n:
                if sum(path) == num:
                    check.append("True")
                return
            else:
                for j in range(i, n):
                    path.append(int(square_string[i:j+1]))
                    dfs(j+1)
                    path.pop()
                    # if len(check) == 0:
                    #     path.append(int(square_string[i:j+1]))
                    #     dfs(j)
                    #     path.pop()
                    # else:
                    #     return
        dfs(0)
        #print("final: {}".format(check))
        if len(check) > 0:
            return True
        else:
            return False

    def punishmentNumber(self, n: int) -> int:
        print(self.check(9, "81"))
        ans = [1]
        if n <= 1:
            return 1
        for i in range(2, n+1):
            if self.check(i, str(i*i)):
                ans.append(i*i)
        return sum(ans)
1370