<p>Given two strings <code>s</code> and <code>t</code>, transform string <code>s</code> into string <code>t</code> using the following operation any number of times:</p>

<ul>
	<li>Choose a <strong>non-empty</strong> substring in <code>s</code> and sort it in place so the characters are in <strong>ascending order</strong>.

	<ul>
		<li>For example, applying the operation on the underlined substring in <code>&quot;1<u>4234</u>&quot;</code> results in <code>&quot;1<u>2344</u>&quot;</code>.</li>
	</ul>
	</li>
</ul>

<p>Return <code>true</code> if <em>it is possible to transform <code>s</code> into <code>t</code></em>. Otherwise, return <code>false</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

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

<pre>
<strong>Input:</strong> s = &quot;84532&quot;, t = &quot;34852&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> You can transform s into t using the following sort operations:
&quot;84<u>53</u>2&quot; (from index 2 to 3) -&gt; &quot;84<u>35</u>2&quot;
&quot;<u>843</u>52&quot; (from index 0 to 2) -&gt; &quot;<u>348</u>52&quot;
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;34521&quot;, t = &quot;23415&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> You can transform s into t using the following sort operations:
&quot;<u>3452</u>1&quot; -&gt; &quot;<u>2345</u>1&quot;
&quot;234<u>51</u>&quot; -&gt; &quot;234<u>15</u>&quot;
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;12345&quot;, t = &quot;12435&quot;
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>s.length == t.length</code></li>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> and <code>t</code> consist of only digits.</li>
</ul>

class BIT():
    def __init__(self, n):
        self.n = n
        self.tree = [0] * (n + 1)

    def sum(self, i):
        ans = 0
        i += 1
        while i > 0:
            ans += self.tree[i]
            i -= (i & (-i))
        return ans

    def update(self, i, value):
        i += 1
        while i <= self.n:
            self.tree[i] += value
            i += (i & (-i))  


class Solution:
    def isTransformable(self, s: str, t: str) -> bool:
        if Counter(s)!=Counter(t):
            return False
        ind = defaultdict(deque)
        for id, i in enumerate(t):
            ind[i].append(id)
        a = []
        for i in s:
            a.append(ind[i].popleft())
        n=len(a)
        bt=BIT(n+1)
        ind=defaultdict(lambda :-1)
        for i in range(n):
            inv=bt.sum(n)-bt.sum(a[i])
            bt.update(a[i],1)
            for dig in range(int(s[i])-1,-1,-1):
                if ind[dig]>=i-inv:
                    return False
            ind[int(s[i])]=i-inv
        return True
23200