<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(length: int) -> List[int]:
            # Initialize comparison list
            comparison_result = [0] * n
            # Compare substrings of the specified length
            for i, (left, right) in enumerate(zip(num[:-length], num[length:])):
                if left < right:
                    # Mark the range [i-length, i) with -1 if the left part is smaller
                    for j in range(i + length, i, -1):
                        if comparison_result[j]: break
                        comparison_result[j] = -1
                elif left > right:
                    # Mark the range [i-length, i) with 1 if the left part is greater
                    for j in range(i + length, i, -1):
                        if comparison_result[j]: break
                        comparison_result[j] = 1
            return comparison_result

        # Length of the input string and modulo constant
        n, mod = len(num), 10**9 + 7
        # Initialize the accumulator and find the positions of zeros
        combinations, zero_positions = [1] + [0] * n, {i for i, digit in enumerate(num) if digit == '0'}

        # Iterate through all possible lengths of the substring
        for length in range(1, n + 1):
            # Create a copy of the combinations array for dynamic programming
            current_combinations = combinations[:]
            # Set the positions with zeros to 0 in the current_combinations array
            for i in zero_positions:
                current_combinations[i] = 0

            if length <= n >> 1:  # Only compare if length is less than or equal to half of n
                comparison_result = compare(length)
                # Update current_combinations based on the comparison results
                for i in range(length, n - length + 1):
                    if i not in zero_positions and comparison_result[i] <= 0:
                        current_combinations[i] += current_combinations[i - length]

            # Update the combinations array with the current_combinations values
            for i in range(length, n + 1):
                combinations[i] = (combinations[i] + current_combinations[i - length]) % mod

        # Return the final result
        return combinations[-1]
1069