<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

        lol = 10**9 + 7
        n = len(num)
        results = [
            [
                0 for j in range(0, n+2)
            ] for i in range(0, n+1)
        ]

        for i in range(0, n+2):
            results[n][i] = 1

        def get_next_take(start_i, take):
            cur_num = num[start_i:start_i+take]
            remaining_places = n - start_i - take
            if remaining_places < take:
                #print("can't continue {} with {}".format(num[start_i:start_i+take], num[start_i+take:]))
                return take + 1
            next_num = num[start_i+take:start_i+take+take]
            if next_num >= cur_num:
                #print("free continue {} with {}".format(num[start_i:start_i+take], num[start_i+take:]))
                return take
            #print("costly continue {} with {}".format(num[start_i:start_i+take], num[start_i+take:]))
            return take + 1

        for start_i in range(n-1, -1, -1):
            if num[start_i] == "0":
                continue
            max_take = n - start_i
            for take in range(max_take, 0, -1):
                results[start_i][take] = results[start_i][take+1]
                next_take = get_next_take(start_i, take)
                results[start_i][take] += results[start_i+take][next_take]
                results[start_i][take] = results[start_i][take] % lol
        return results[0][1]
2811