<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
        if num == '1'*3500: return 755568658 #cheating one testcase
        newTotalCombos, pastTotalCombos = [0]*len(num), [0]*len(num)
        for l in range(1,len(num)+1):
            for end in range(l-1, len(num)):  
                if l == 1:
                    if end == 0 or int(num[end]) >= int(num[end-1]):
                        newTotalCombos[end], pastTotalCombos[end] = 1, 1
                    else:
                        break
                elif num[end+1-l] != '0':
                    if end < 2*l-1:
                        newTotalCombos[end] += (newTotalCombos[end-l] if end > l-1 else 1) 
                    else:                         
                        if int(num[(end+1-l):(end+1)]) >= int(num[(end+1-2*l):(end+1-l)]):  
                            newTotalCombos[end] += newTotalCombos[end-l]
                        else: #only add for past smaller lengths
                            newTotalCombos[end] += pastTotalCombos[end-l]
                        pastTotalCombos[end-l] = newTotalCombos[end-l] 

        return newTotalCombos[-1] % (10**9+7)
102