<p>Given a binary string <code>s</code>, partition the string into one or more <strong>substrings</strong> such that each substring is <strong>beautiful</strong>.</p>

<p>A string is <strong>beautiful</strong> if:</p>

<ul>
	<li>It doesn&#39;t contain leading zeros.</li>
	<li>It&#39;s the <strong>binary</strong> representation of a number that is a power of <code>5</code>.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> number of substrings in such partition. </em>If it is impossible to partition the string <code>s</code> into beautiful substrings,&nbsp;return <code>-1</code>.</p>

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

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

<pre>
<strong>Input:</strong> s = &quot;1011&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can paritition the given string into [&quot;101&quot;, &quot;1&quot;].
- The string &quot;101&quot; does not contain leading zeros and is the binary representation of integer 5<sup>1</sup> = 5.
- The string &quot;1&quot; does not contain leading zeros and is the binary representation of integer 5<sup>0</sup> = 1.
It can be shown that 2 is the minimum number of beautiful substrings that s can be partitioned into.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;111&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can paritition the given string into [&quot;1&quot;, &quot;1&quot;, &quot;1&quot;].
- The string &quot;1&quot; does not contain leading zeros and is the binary representation of integer 5<sup>0</sup> = 1.
It can be shown that 3 is the minimum number of beautiful substrings that s can be partitioned into.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;0&quot;
<strong>Output:</strong> -1
<strong>Explanation:</strong> We can not partition the given string into beautiful substrings.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 15</code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

import math
class Solution:
    def minimumBeautifulSubstrings(self, s: str) -> int:
        def call(string,selected,target):
            if target==3:
                print(selected)

            if len(selected)==target-1:
                if (5**(int(math.log(int(string,2),5)))==int(string,2) or int(string,2)==1) and (not string.startswith("0") or len(string)==1):
                    return True
                else:
                    selected.pop()
                    return False

            for x in range(1,len(string)):
                if not string[:x].startswith("0") or len(string[:x])==1:
                    print(int(string[:x],2),math.log(25,5))
                    try:
                        if 5**(int(math.log(int(string[:x],2),5)))==int(string[:x],2) or int(string[:x],2)==1:
                            selected.append(string[:x])
                            val=call(string[x:],selected,target)
                            if val is True:
                                return True
                            else:
                                pass
                        else:
                            pass
                    except:
                        pass

            if selected!=[]:
                selected.pop()
        for x in range(2,len(s)+1):
            if call(s,[],x):
                print(x,"+++++++")
                return x
            else:
                print(x,"_----------")
                pass
        try:
            if 5**(int(math.log(int(s,2),5)))==int(s,2) and (not s.startswith("0") or len(s)==1):
                return 1
            else:
                return -1
        except:
            return -1



        
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