<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

    kMod = 1_000_000_007
    n = len(num)
    # dp[i][k] := the number of possible lists of integers ending in num[i]
    # with the length of the last number being 1..k
    dp = [[0] * (n + 1) for _ in range(n)]
    # lcs[i][j] := the number of the same digits in num[i..n) and num[j..n)
    lcs = [[0] * (n + 1) for _ in range(n + 1)]

    for i in range(n - 1, -1, -1):
      for j in range(i + 1, n):
        if num[i] == num[j]:
          lcs[i][j] = lcs[i + 1][j + 1] + 1

    for i in range(n):
      for k in range(1, i + 2):
        dp[i][k] += dp[i][k - 1]
        dp[i][k] %= kMod
        # The last number is num[s..i].
        s = i - k + 1
        if num[s] == '0':
          # the number of possible lists of integers ending in num[i] with the
          # length of the last number being k
          continue
        if s == 0:  # the whole string
          dp[i][k] += 1
          continue
        if s < k:
          # The length k is not enough, so add the number of possible lists of
          # integers in num[0..s - 1].
          dp[i][k] += dp[s - 1][s]
          continue
        l = lcs[s - k][s]
        if l >= k or num[s - k + l] <= num[s + l]:
          # Have enough length k and num[s - k..s - 1] <= num[j..i].
          dp[i][k] += dp[s - 1][k]
        else:
          # Have enough length k but num[s - k..s - 1] > num[j..i].
          dp[i][k] += dp[s - 1][k - 1]

    return dp[n - 1][n] % kMod
2885