<p>Given two strings <code>s</code> and <code>t</code>, <em>determine if they are isomorphic</em>.</p>

<p>Two strings <code>s</code> and <code>t</code> are isomorphic if the characters in <code>s</code> can be replaced to get <code>t</code>.</p>

<p>All occurrences of a character must be replaced with another character while preserving the order of characters. No two characters may map to the same character, but a character may map to itself.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;egg&quot;, t = &quot;add&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">true</span></p>

<p><strong>Explanation:</strong></p>

<p>The strings <code>s</code> and <code>t</code> can be made identical by:</p>

<ul>
	<li>Mapping <code>&#39;e&#39;</code> to <code>&#39;a&#39;</code>.</li>
	<li>Mapping <code>&#39;g&#39;</code> to <code>&#39;d&#39;</code>.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;foo&quot;, t = &quot;bar&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">false</span></p>

<p><strong>Explanation:</strong></p>

<p>The strings <code>s</code> and <code>t</code> can not be made identical as <code>&#39;o&#39;</code> needs to be mapped to both <code>&#39;a&#39;</code> and <code>&#39;r&#39;</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;paper&quot;, t = &quot;title&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">true</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>t.length == s.length</code></li>
	<li><code>s</code> and <code>t</code> consist of any valid ascii character.</li>
</ul>

class Solution:
    def isIsomorphic(self, s: str, t: str) -> bool:
        dictionary1 = collections.defaultdict(str)
        dictionary2 = collections.defaultdict(str)

        if len(s) != len(t): return False
        for i in range(len(s)):
            dictionary1[s[i]] += str(i)
            dictionary2[t[i]] += str(i)
        
        
        for first, second in zip(dictionary1, dictionary2):
            if dictionary1[first] != dictionary2[second]:
                return False
        return True
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