<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:

        def compare(d: int) -> List[int]:
            comp = [0]*n
            for i, (l,r) in enumerate(zip(num[:-d], num[d:])):
                if l < r:
                    for j in range(i+d,i,-1):
                        if comp[j]: break
                        comp[j] = -1
                elif l > r:
                    for j in range(i+d,i,-1):
                        if comp[j]: break
                        comp[j] = 1
            return comp

        n, mod = len(num), 10**9+7
        acc, zeros = [1]+[0]*n, set(i for i,dig in enumerate(num) if dig=='0')

        for d in range(1,n+1):
            dp = acc[:]
            for i in zeros:
                dp[i] = 0
            if d <= n>>1:
                comp = compare(d)
                for i in range(d, n-d+1):
                    if i not in zeros and comp[i] <= 0:
                        dp[i] += dp[i-d]
            for i in range(d,n+1):
                acc[i] = (acc[i] + dp[i-d]) % mod
        return acc[-1]
1085