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
function punishmentNumber(n: number): number {
    const check = (s: string, i: number, x: number): boolean => {
        const m = s.length;
        if (i >= m) {
            return x === 0;
        }
        let y = 0;
        for (let j = i; j < m; ++j) {
            y = y * 10 + Number(s[j]);
            if (y > x) {
                break;
            }
            if (check(s, j + 1, x - y)) {
                return true;
            }
        }
        return false;
    };
    let ans = 0;
    for (let i = 1; i <= n; ++i) {
        const x = i * i;
        const s = x.toString();
        if (check(s, 0, i)) {
            ans += x;
        }
    }
    return ans;
}
