<p>You are given two arrays with <strong>positive</strong> integers <code>arr1</code> and <code>arr2</code>.</p>

<p>A <strong>prefix</strong> of a positive integer is an integer formed by one or more of its digits, starting from its <strong>leftmost</strong> digit. For example, <code>123</code> is a prefix of the integer <code>12345</code>, while <code>234</code> is <strong>not</strong>.</p>

<p>A <strong>common prefix</strong> of two integers <code>a</code> and <code>b</code> is an integer <code>c</code>, such that <code>c</code> is a prefix of both <code>a</code> and <code>b</code>. For example, <code>5655359</code> and <code>56554</code> have a common prefix <code>565</code> while <code>1223</code> and <code>43456</code> <strong>do not</strong> have a common prefix.</p>

<p>You need to find the length of the <strong>longest common prefix</strong> between all pairs of integers <code>(x, y)</code> such that <code>x</code> belongs to <code>arr1</code> and <code>y</code> belongs to <code>arr2</code>.</p>

<p>Return <em>the length of the <strong>longest</strong> common prefix among all pairs</em>.<em> If no common prefix exists among them</em>, <em>return</em> <code>0</code>.</p>

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

<pre>
<strong>Input:</strong> arr1 = [1,10,100], arr2 = [1000]
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are 3 pairs (arr1[i], arr2[j]):
- The longest common prefix of (1, 1000) is 1.
- The longest common prefix of (10, 1000) is 10.
- The longest common prefix of (100, 1000) is 100.
The longest common prefix is 100 with a length of 3.
</pre>

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

<pre>
<strong>Input:</strong> arr1 = [1,2,3], arr2 = [4,4,4]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There exists no common prefix for any pair (arr1[i], arr2[j]), hence we return 0.
Note that common prefixes between elements of the same array do not count.
</pre>

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

<ul>
	<li><code>1 &lt;= arr1.length, arr2.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= arr1[i], arr2[i] &lt;= 10<sup>8</sup></code></li>
</ul>

class Solution:
    def longestCommonPrefix(self, arr1: List[int], arr2: List[int]) -> int:
        def countCommon(x, y):
            count = 0
            i = 0
            while i < len(x) and i < len(y):
                if x[i] == y[i]:
                    count += 1
                    i += 1
                else:
                    break
            return count
        arr1.sort(key=lambda x:str(x))
        arr2.sort(key=lambda y:str(y))
        i, j = 0, 0
        max_common = 0
        while i < len(arr1) and j < len(arr2):
            max_common = max(max_common, countCommon(str(arr1[i]), str(arr2[j])))
            if str(arr1[i]) < str(arr2[j]):
                i += 1
            else:
                j += 1
        return max_common


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