<p>You wrote down many <strong>positive</strong> integers in a string called <code>num</code>. However, you realized that you forgot to add commas to seperate the different numbers. You remember that the list of integers was <strong>non-decreasing</strong> and that <strong>no</strong> integer had leading zeros.</p>

<p>Return <em>the <strong>number of possible lists of integers</strong> that you could have written down to get the string </em><code>num</code>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> num = &quot;327&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> You could have written down the numbers:
3, 27
327
</pre>

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

<pre>
<strong>Input:</strong> num = &quot;094&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong> No numbers can have leading zeros and all numbers must be positive.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;0&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong> No numbers can have leading zeros and all numbers must be positive.
</pre>

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

<ul>
	<li><code>1 &lt;= num.length &lt;= 3500</code></li>
	<li><code>num</code> consists of digits <code>&#39;0&#39;</code> through <code>&#39;9&#39;</code>.</li>
</ul>

class Solution:
    def numberOfCombinations(self, num: str) -> int:
        if num[0] == '0': return 0
        
        mod, n = 10**9 + 7, len(num)
        same = [[0] * (n+1) for _ in range(n+1)]
        
        range_down = range(n-1, -1, -1)
        range_down_n = range(n, 0, -1)
        
        for i in range_down:
            for j in range_down:
                if num[i] == num[j]: same[i][j] = same[i+1][j+1] + 1
        
        dp = [[0] * (n+2) for _ in range_down]
        for i in range_down:
            for j in range_down_n:
                if num[i] == '0' or i+j > n: continue
                if i+j == n: dp[i][j] = 1
                if i+j+1 <= n: dp[i][j] = dp[i][j+1] % mod
                p = same[i][i+j]
                if p >= j or (i + j + p < n and num[i + p] <= num[i + j + p]):
                    dp[i][j] = (dp[i][j] + dp[i+j][j]) % mod
                elif i + 2 * j + 1 <= n:
                    dp[i][j] = (dp[i][j] + dp[i+j][j+1]) % mod

        return dp[0][1]        
3107