<p>Given two positive integers <code>low</code> and <code>high</code> represented as strings, find the count of <strong>stepping numbers</strong> in the inclusive range <code>[low, high]</code>.</p>

<p>A <strong>stepping number</strong> is an integer such that all of its adjacent digits have an absolute difference of <strong>exactly</strong> <code>1</code>.</p>

<p>Return <em>an integer denoting the count of stepping numbers in the inclusive range</em> <code>[low, high]</code><em>. </em></p>

<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p><strong>Note:</strong> A stepping number should not have a leading zero.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> low = &quot;1&quot;, high = &quot;11&quot;
<strong>Output:</strong> 10
<strong>Explanation: </strong>The stepping numbers in the range [1,11] are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. There are a total of 10 stepping numbers in the range. Hence, the output is 10.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> low = &quot;90&quot;, high = &quot;101&quot;
<strong>Output:</strong> 2
<strong>Explanation: </strong>The stepping numbers in the range [90,101] are 98 and 101. There are a total of 2 stepping numbers in the range. Hence, the output is 2. </pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= int(low) &lt;= int(high) &lt; 10<sup>100</sup></code></li>
	<li><code>1 &lt;= low.length, high.length &lt;= 100</code></li>
	<li><code>low</code> and <code>high</code> consist of only digits.</li>
	<li><code>low</code> and <code>high</code> don&#39;t have any leading zeros.</li>
</ul>

class Solution:
    def countSteppingNumbers(self, low: str, high: str) -> int:
        mod = 10 ** 9 + 7
        dp = [[[[-1 for _ in range(2)] for _ in range(2)] for _ in range(11)] for _ in range(101)]

        def count_step_number(upper, pos, tight, prev, all_zero): 
            nonlocal mod
            nonlocal dp
            if pos == len(upper):
                return 1 - all_zero

            if dp[pos][prev+1][tight][all_zero] != -1:
                return dp[pos][prev+1][tight][all_zero]
            
            limit = int(upper[pos])
            if not tight:
                limit = 9
            ans = 0
            for i in range(limit + 1):
                n_tight = 1 if i == limit and tight == 1 else 0
                n_all_zero = 1 if all_zero ==1 and i == 0 else 0
                if all_zero or abs(i - prev) == 1:
                    ans = (ans + count_step_number(upper, pos+1, n_tight, i, n_all_zero)) % mod
            dp[pos][prev+1][tight][all_zero] = ans 
            return ans
        
        def reset_dp():
            nonlocal dp
            for i in range(101):
                for j in range(11):
                    for k in range(2):
                        for l in range(2):
                            dp[i][j][k][l] = -1

        upper_count = count_step_number(high, 0, 1, -1, 1) 
        reset_dp()
        lower_count = count_step_number(str(int(low) - 1), 0, 1, -1, 1) 
        return (upper_count - lower_count) % mod

    
            

            
22000