<p>Given two strings: <code>s1</code> and <code>s2</code> with the same&nbsp;size, check if some&nbsp;permutation of string <code>s1</code> can break&nbsp;some&nbsp;permutation of string <code>s2</code> or vice-versa. In other words <code>s2</code> can break <code>s1</code>&nbsp;or vice-versa.</p>

<p>A string <code>x</code>&nbsp;can break&nbsp;string <code>y</code>&nbsp;(both of size <code>n</code>) if <code>x[i] &gt;= y[i]</code>&nbsp;(in alphabetical order)&nbsp;for all <code>i</code>&nbsp;between <code>0</code> and <code>n-1</code>.</p>

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

<pre>
<strong>Input:</strong> s1 = &quot;abc&quot;, s2 = &quot;xya&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> &quot;ayx&quot; is a permutation of s2=&quot;xya&quot; which can break to string &quot;abc&quot; which is a permutation of s1=&quot;abc&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s1 = &quot;abe&quot;, s2 = &quot;acd&quot;
<strong>Output:</strong> false 
<strong>Explanation:</strong> All permutations for s1=&quot;abe&quot; are: &quot;abe&quot;, &quot;aeb&quot;, &quot;bae&quot;, &quot;bea&quot;, &quot;eab&quot; and &quot;eba&quot; and all permutation for s2=&quot;acd&quot; are: &quot;acd&quot;, &quot;adc&quot;, &quot;cad&quot;, &quot;cda&quot;, &quot;dac&quot; and &quot;dca&quot;. However, there is not any permutation from s1 which can break some permutation from s2 and vice-versa.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s1 = &quot;leetcodee&quot;, s2 = &quot;interview&quot;
<strong>Output:</strong> true
</pre>

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

<ul>
	<li><code>s1.length == n</code></li>
	<li><code>s2.length == n</code></li>
	<li><code>1 &lt;= n &lt;= 10^5</code></li>
	<li>All strings consist of lowercase English letters.</li>
</ul>

class Solution:
    def checkIfCanBreak(self, s1: str, s2: str) -> bool:
        # Sort both strings
        sorted_s1 = sorted(s1)
        sorted_s2 = sorted(s2)
        
        # Check if sorted_s1 can break sorted_s2
        can_s1_break_s2 = True
        can_s2_break_s1 = True
        
        for i in range(len(s1)):
            if sorted_s1[i] < sorted_s2[i]:
                can_s1_break_s2 = False
            if sorted_s2[i] < sorted_s1[i]:
                can_s2_break_s1 = False
        
        # Return true if either can break the other
        return can_s1_break_s2 or can_s2_break_s1

# Example usage:
# solution = Solution()
# print(solution.checkIfCanBreak("abc", "xya"))  # Output: True
# print(solution.checkIfCanBreak("abe", "acd"))  # Output: False
# print(solution.checkIfCanBreak("leetcodee", "interview"))  # Output: True
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