<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:
        n = len(num)
        lcs = [[0]*(n+1) for _ in range(n)]
        for i in reversed(range(n)): 
            for j in reversed(range(i+1, n)): 
                if num[i] == num[j]: lcs[i][j] = 1 + lcs[i+1][j+1]
        
        def cmp(i, j, d): 
            """Return True if """
            m = lcs[i][j]
            if m >= d: return True 
            return num[i+m] <= num[j+m]
        
        dp = [[0]*(n+1) for _ in range(n)]
        for i in range(n): 
            if num[i] != "0": 
                for j in range(i+1, n+1): 
                    if i == 0: dp[i][j] = 1
                    else: 
                        dp[i][j] = dp[i][j-1]
                        if 2*i-j >= 0 and cmp(2*i-j, i, j-i): dp[i][j] += dp[2*i-j][i]
                        if 2*i-j+1 >= 0 and not cmp(2*i-j+1, i, j-i-1): dp[i][j] += dp[2*i-j+1][i]
        return sum(dp[i][n] for i in range(n)) % 1_000_000_007
2554