<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
        MOD = 10**9+7
        n = len(num)
        # longest common prefix
        lcp = [[0]*(n+1) for _ in range(n+1)]
        for i in range(n-1, -1, -1):
            for j in range(i):
                if num[i] == num[j]:
                    lcp[j][i] = lcp[j+1][i+1] + 1
        # dp[i][j] => last number is num[i:j+1]
        dp = [[0]*n for _ in range(n)]
        for i in range(n):
            if num[i] == '0': continue
            cur = 1 if i == 0 else 0
            for j in range(i, n):
                length = j - i + 1
                dp[i][j] = cur
                if i >= length:
                    lcp_l = lcp[i-length][i]
                    if lcp_l >= length or (lcp_l < length and num[i-length+lcp_l] < num[i+lcp_l]):
                        dp[i][j] += dp[i-length][i-1]
                    cur += dp[i-length][i-1]
                dp[i][j] %= MOD
        return sum(dp[i][-1] for i in range(n)) % MOD
2140