<p>You are given an array <code>arr</code> which consists of only zeros and ones, divide the array into <strong>three non-empty parts</strong> such that all of these parts represent the same binary value.</p>

<p>If it is possible, return any <code>[i, j]</code> with <code>i + 1 &lt; j</code>, such that:</p>

<ul>
	<li><code>arr[0], arr[1], ..., arr[i]</code> is the first part,</li>
	<li><code>arr[i + 1], arr[i + 2], ..., arr[j - 1]</code> is the second part, and</li>
	<li><code>arr[j], arr[j + 1], ..., arr[arr.length - 1]</code> is the third part.</li>
	<li>All three parts have equal binary values.</li>
</ul>

<p>If it is not possible, return <code>[-1, -1]</code>.</p>

<p>Note that the entire part is used when considering what binary value it represents. For example, <code>[1,1,0]</code> represents <code>6</code> in decimal, not <code>3</code>. Also, leading zeros <strong>are allowed</strong>, so <code>[0,1,1]</code> and <code>[1,1]</code> represent the same value.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> arr = [1,0,1,0,1]
<strong>Output:</strong> [0,3]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> arr = [1,1,0,1,1]
<strong>Output:</strong> [-1,-1]
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> arr = [1,1,0,0,1]
<strong>Output:</strong> [0,2]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= arr.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>arr[i]</code> is <code>0</code> or <code>1</code></li>
</ul>

class Solution:
    def threeEqualParts(self, arr: List[int]) -> List[int]:

        # Step 1: Count total number of 1's in the array
        total_ones = arr.count(1)

        # If total number of 1's is not divisible by 3, return [-1, -1]
        if total_ones % 3 != 0:
            return [-1, -1]

        if total_ones == 0:
            return [0, len(arr)-1]


        # Step 2: Find the indices of the first 1's in the three parts
        ones_per_part = total_ones // 3
        first, second, third = -1, -1, -1
        ones_count = 0

        for i in range(0, len(arr)):
            if arr[i] == 1:
                ones_count += 1
                if (ones_count == 1):
                    first = i
                elif (ones_count == ones_per_part +1 ):
                    second = i
                elif (ones_count == 2*ones_per_part +1 ):
                    third = i
                    break
        
        while third < len(arr) and arr[first] == arr[second] and arr[second]== arr[third]:
            first+=1
            second+=1
            third+=1

        if third == len(arr):
            return [first-1,second]
        else:
            return [-1, -1]


        
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